Cho các số nguyên \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) thỏa mãn \(a+\frac{b+\log _{2} 5}{c+\log _{2} 3}=\log _{6} 45\). Tổng \(a+b+c\) bằng
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Phương pháp giải
Sử dụng các công thức:
\(\log _{a} b=\frac{\log _{c} b}{\log _{c} a}(0<a, c \neq 1, b>0)\)
\(\log _{a}(x y)=\log _{a} x+\log _{a} y(0<a \neq 1, x, y>0)\)
\(\log _{a^{n}} b^{m}=\frac{m}{n} \log _{a} b(0<a \neq 1, b>0)\)
Lời giải
Ta có: \(a+\frac{b+\log _{2} 5}{c+\log _{2} 3}=\log _{6} 45 \Leftrightarrow a+\frac{b+\log _{2} 5}{c+\log _{2} 3}=\frac{\log _{2} 45}{\log _{2} 6}\)
\(\Leftrightarrow \mathrm{a}+\frac{\mathrm{b}+\log _{2} 5}{\mathrm{c}+\log _{2} 3}=\frac{\log _{2}\left(3^{2} .5\right)}{\log _{2}(2.3)} \Leftrightarrow \mathrm{a}+\frac{\mathrm{b}+\log _{2} 5}{\mathrm{c}+\log _{2} 3}=\frac{2 \log _{2} 3+\log _{2} 5}{1+\log _{2} 3}\)
\(\Leftrightarrow \mathrm{a}+\frac{\mathrm{b}+\log _{2} 5}{\mathrm{c}+\log _{2} 3}=\frac{2+2 \log _{2} 3-2+\log _{2} 5}{1+\log _{2} 3}\)
\(\Leftrightarrow \mathrm{a}+\frac{\mathrm{b}+\log _{2} 5}{\mathrm{c}+\log _{2} 3}=2+\frac{-2+\log _{2} 5}{1+\log _{2} 3}\)
Đồng nhất hệ số ta có \(a=2, b=-2, c=1\).
Vậy \(a+b+c=2+(-2)+1=1\).
Đề Thi Tham Khảo Đánh Giá Năng Lực Năm 2025 – ĐHQG Hà Nội – Đề Số 1 là tài liệu ôn tập quan trọng giúp học sinh làm quen với cấu trúc và dạng câu hỏi của kỳ thi ĐGNL do Đại học Quốc gia Hà Nội tổ chức. Đề thi bao gồm các câu hỏi đa dạng, đánh giá toàn diện năng lực tư duy, kiến thức tổng hợp và khả năng giải quyết vấn đề. Tài liệu này giúp thí sinh rèn luyện kỹ năng làm bài, nâng cao hiệu suất làm bài thi và chuẩn bị tốt nhất cho kỳ thi chính thức năm 2025.
Câu hỏi liên quan
Read the following passage and mark the letter A, B, C, or D to indicate the correct word or phrase that best fits each the numbered blanks from 31 to 35.
“One month on since the devastating earthquake hit Türkiye and Syria, the scale of the humanitarian response has yet to meet the enormous needs of displaced Syrian families and children (31)_____have suffered from compounded crises for almost 12 years now,” said Johan Mooij, director of World Vision’s Syria crisis response. “It is crucial that (32)_____ access channels to northwest Syria remain open, and that aid deliveries are scaled up through earmarked funding for the emergency response. Only this will ensure that children’s mental health needs are covered, and their trauma addressed.”
Snow and bitter winter weather have placed children at great risk of hypothermia (33)_____ they struggle to survive in sub-zero temperatures. Many survivors have had to sleep in cars, outside, or in makeshift shelters. Doctors (34)_____ that children are also at risk of exposure to waterborne diseases such as cholera or Hepatitis A due to the damage to shelters and water infrastructure.
These children are now even more vulnerable to family separation, exploitation, and abuse. As buildings are deemed unsafe, they also are unable to return to school.
“In northern Syria, in particular, the threats to children from abuse were already extreme. The soaring poverty, within a warzone, now devastated by earthquakes, has created an unimaginable number of challenges, and suffering for children,” says Johan, director of the Syria crisis response in Amman, Jordan. “This earthquake has created the perfect environment for a health crisis -fueled by reduced healthcare capacity and disease (35)_____.”
Ampe kế có giới hạn đo là 50 mA phù hợp để đo cường độ dòng điện nào dưới đây?
Read the following advertisement and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 1 to 6.
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Cực đại của hàm số \(y=\sqrt{8+2 x-x^{2}}\) bằng bao nhiêu?
Động lực chính của các cuộc cách mạng tư sản là
Read the following passage about Unconventional Teachers Who Changed Lives and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 23 to 30.
Traditional education focuses on textbooks, but some teachers go beyond these limitations. Mrs. Rodriguez transformed her classroom into a living laboratory. Her students conducted experiments with plants and simple machines. She believed hands-on learning creates deeper understanding than reading alone. When asked why she taught differently, she replied, "I want students to fall in love with discovery." Her methods helped struggling students improve and develop passion for science.
Mr. Jackson abandoned lectures for storytelling and role-playing. His students experienced history by acting out important moments. This approach made history come alive and helped them remember key information. One student said, "Before Mr. Jackson's class, I thought history was boring, but he showed us it's fascinating." He took classes to historical sites and invited veterans to share experiences. These connections helped students understand how past shapes our present.
In a remote village, Ms. Chen taught English without proper textbooks. She created materials using newspapers and song lyrics. Despite limited resources, her students achieved remarkable results through her dedication. "Learning should be joyful, not painful," she told questioning parents. Ms. Chen organized conversation clubs and pen pal exchanges. These activities gave students practical language skills and confidence to use English in real situations.
Coach Williams was a life mentor who taught valuable lessons through sports. He focused on teamwork and fair play rather than winning. Students who struggled academically often excelled in his class. "The playing field is where children learn who they truly are," he explained. He created inclusive activities for all students regardless of athletic ability. Many former students credit him with teaching life skills like resilience and cooperation that helped them succeed after graduation.
In which paragraph does the writer mention Coach Williams taught valuable life lessons through physical education?
Read the following passage about the cultural diversity and mark the letter A, B, C or D on your answer sheet to indicate the best answer to each of the following questions from 1 to 10.
[I] In today's globalized world, cultural diversity has become a fundamental aspect of many societies. [II] Many countries are experiencing increasing levels of migration. [III] With the rise of immigration and the blending of traditions, people from various cultural backgrounds are now living side by side in cities across the globe. [IV]
One of the key advantages of cultural diversity is the richness that it adds to a society. Different cultures introduce unique viewpoints, foods, languages, and traditions, which help people broaden their understanding of the world. In schools and workplaces, cultural diversity fosters creativity and innovation, as individuals from different backgrounds approach problems in innovative ways. However, there are also challenges associated with living in culturally diverse communities. Misunderstandings and communication barriers can arise when people are unfamiliar with each other's customs and values. To address these issues, societies must encourage cultural sensitivity and create opportunities for cross-cultural exchange.
Governments and institutions around the world are beginning to implement policies that promote inclusion and respect for cultural differences. By celebrating diversity through events, education, and media representation, communities can create environments where people feel valued regardless of their background. Ultimately, embracing cultural diversity helps to build more peaceful and harmonious societies.
The word “innovative” in paragraph 2 could best be replaced by _______.
Muốn quan sát hình dạng và kích thước tế bào thực vật, chúng ta cần dùng dụng cụ nào sau đây?
Chủ thể sản xuất cần phải có những trách nhiệm gì?
Read the following passage and mark the letter A, B, C or D on your answer sheet to indicate the correct answer to each of the questions:
For many people who live in cities, parks are an important part of the landscape. They provide a place for people to relax and play sports, as well as a refuge from the often harsh environment of a city. What people often overlook is that parks also provide considerable environmental benefits.
One benefit of parks is that plants absorb carbon dioxide - a key pollutant - and emit oxygen, which humans need to breathe. According to one study, an acre of trees can absorb the same amount of carbon dioxide that a typical car emits in 11,000 miles of driving. Parks also make cities cooler. Scientists have long noted what is called the Urban Heat Island Effect: building materials such as metal, concrete, and asphalt absorb much more of the sun’s heat and release it much more quickly than organic surfaces like trees and grass. Because city landscapes contain so much of these building materials, cities are usually warmer than surrounding rural areas. Parks and other green spaces help to mitigate the Urban Heat Island Effect.
Unfortunately, many cities cannot easily create more parks because most land is already being used for buildings, roads, parking lots, and other essential parts of the urban environment. However, cities could benefit from many of the positive effects of parks by encouraging citizens to create another type of green space: rooftop gardens. While most people would not think of starting a garden on their roof, human beings have been planting gardens on rooftops for thousands of years. Some rooftop gardens are very complex and require complicated engineering, but others are simple container gardens that anyone can create with the investment of a few hundred dollars and a few hours of work.
Rooftop gardens provide many of the same benefits as other urban park and garden spaces, but without taking up the much-needed land. Like parks, rooftop gardens help to replace carbon dioxide in the air with nourishing oxygen. They also help to lessen the Urban Heat Island Effect, which can save people money.
In the summer, rooftop gardens prevent buildings from absorbing heat from the sun, which can significantly reduce cooling bills. In the winter, gardens help hold in the heat that materials like brick and concrete radiate so quickly, leading to savings on heating bills. Rooftop vegetable and herb gardens can also provide fresh food for city dwellers, saving them money and making their diets healthier. Rooftop gardens are not only something everyone can enjoy, they are also a smart environmental investment.
Question 36: Based on its use in paragraph 2, it can be inferred that mitigate belongs to which of the following word groups?
Trong những nhận dịnh sau, nhận định nào đúng, nhận định nào sai khi nói về câu văn dưới đây?
Nguyễn Du được sinh ra trong một gia đình có truyền thống văn chương và nhiều đời làm quan nên Nguyễn Du đã được thừa hưởng năng khiếu văn chương ngay từ khi còn rất nhỏ.
CHỦ ĐỀ: CHẾ TẠO BÊ TÔNG NHẸ CÓ KHẢ NĂNG CÁCH NHIỆT VÀ CHỊU LỰC
(Tham khảo bài văn của chủ đề trong đường link dưới đây ở trang 21)
https://tvsthpt.dlib.vn/app/doc-sach-ebook/d0f7e16b522f
Và trả lời câu hỏi sau:
Theo đoạn [2], phương án nào sau đây là thành phẩm trực tiếp của máy nghiền tái chế vật liệu xây dựng?
Phát biểu nào không đúng với quá trình vận chuyển?
- Trong không gian với hệ tọa độ Oxyz, mặt cầu tâm \({\rm{I}}(9; - 8;7)\) bán kính 16 có phương trình là
Nguyên tố nào dưới đây là thành phần quan trọng của hemoglobin trong hồng cầu với chức năng vận chuyển O2?
Đạo hàm của hàm số \(f\left( x \right)=\sqrt{\text{ln}\left( \text{ln}x \right)}\) là:
Read the following leaflet and mark the letter A, B, C or D on your answer sheet to indicate the option that best fits each of the numbered blanks from 7 to 12.
Eat Well, Live Well: Simple Steps for Better Health
Learn how small changes in your diet can make a big difference.
Common issues we face:
We tend to ___(7)___ too much sugar and processed food today, which can lead to health problems. Another challenge is finding time to prepare meals at home, causing a reliance on fast food. Over time, this habit increases the risk of obesity and ___(8)___ diseases.
What we can do:
● ___(9)___ on sugary drinks and replace them with water or herbal tea. This helps reduce excess calories.
● Prepare meals at home ___(10)___ buying pre-made options, giving you control over ___(11)___ and portion sizes.
● When shopping, look for fresh fruits and vegetables rather than processed foods. They provide a(n) ___(12)___ of nutrients essential for good health.
Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the best answer to each of the following questions from 31 to 40.
Working on Your Workout
(I) Although appreciating a balanced diet and regular exercise, most people do not know how to exercise properly. Consequently, they usually rush through their workouts, or they make the same common workout mistakes. (II) Exercising the right way is important for people who are worried about their health and their appearance. (III) However, if someone is not working out properly, they will not see the results they want. Therefore, training experts have devised tips to teach people how to exercise correctly in order to achieve the greatest health benefits. (VI)
One of the most common workout mistakes is doing the same routine over and over again. This does not challenge your muscles, and it can actually prevent muscles from growing and repairing themselves. Instead of always sticking to the same old workout, it is important to change your routine every six to eight weeks. It is also important to add a variety of workouts to your routine, such as swimming, yoga, or biking, to make sure your whole body stays fit. This will help make your workouts more interesting, and benefit your health and muscle development as well.
Another mistake people tend to make is to work out too hard, too often. Your body needs to rest between workouts; otherwise, no progress will be made. It is best to keep the number of hard workout routines to no more than two per week. Then, for those who don’t want to get off schedule by skipping a day, shorter workouts of about twenty minutes can be used on other days. For more variety in workouts, you could also plan an easier routine for forty to sixty minutes between days of shorter, more intense workouts. Experts recommend, however, taking at least one day off completely each week, especially after several hard workout days in a row.
In reality, no one is perfect. However, if you want to make a difference in your overall health, there are some things you can do. Stretch before and after every workout. Do not rush your routine, and do not work out too little or too much. Remember not to make these common workout mistakes, and always have fun while exercising!
The phrase "in a row" is OPPOSITE in meaning to_____:
Nhận định nào sau đây không đúng với các nước đang phát triển?
Tôi mồ côi cha năm hai tuổi
Mẹ tôi thương con không lấy chồng
Trồng dâu, nuôi tằm, dệt vải
Nuôi tôi đến ngày lớn khôn.
Hai mươi năm qua tôi vẫn nhớ
Ngày ấy tôi mới lên năm
Có lần tôi nói dối mẹ
Hôm sau tưởng phải ăn đòn.
Nhưng không, mẹ tôi chỉ buồn
Ôm tôi hôn lên mái tóc
- Con ơi
trước khi nhắm mắt
Cha con dặn con suốt đời
Phải làm một người chân thật…
(Trích Lời mẹ dặn – Phùng Quán)
Nêu giá trị nghệ thuật tiêu biểu nhất của đoạn trích?