Question:
If log (2a × 3b × 5C) is the arithmetic mean of log (22 × 33 × 5), log (26 × 3 × 57 ), and log (2 × 32 × 54 ), then a equals
If log (2a × 3b × 5C) is the arithmetic mean of log (22 × 33 × 5), log (26 × 3 × 57 ), and log (2 × 32 × 54 ), then a equals
Updated On: Sep 26, 2024
- 4
- 5
- 3
- 2
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
log(2a×3b×5c) = 1/3[log (22×33×5) + log (26×3×57) + log (2×32×54)]
log(2a3b5c) = 1/3 [log(22×32×5×26×3×57×2×32×54]
log(2a3b5c) = 1/3[log(29×36×512)]
log(2a3b5c) = log(23×32×54)
Explanation:-
While it is not explicitly stated that a, b and c are integers, going by the spirit of the question, we are forced to assume that they are integers. In that case, we can equate the powers of 2, 3 and 5 on the LHS and the RHS and say that a= 3, b = 2, and c = 4.
Was this answer helpful?
0
0
Top Questions on Logarithms
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- Consider the equation, \(log_5(x-2) = 2log_{25}(2x-4)\) where x is a real number.
For how many different values of x does the given equation hold? - X is a +ve real no, 4 log10 (x) + 4log 100 (x) + 8 log1000 (x) = 13, then the greatest integer not exceeding 'x'
- If \(a\), \(b\), and \(c\) are positive real numbers such that \(a > 10 \ge b \ge c\) and\[ \frac{\log_8(a+b)}{\log_2 c} + \frac{\log_{27}(a-b)}{\log_3 c} = \frac{2}{3} \]then the greatest possible integer value of \(a\) is
- Let $x$ be a positive real number such that $4 \log_{10} x + 4 \log_{100} x + 8 \log_{1000} x = 13$ , then the greatest integer not exceeding $x$. is
View More Questions
Questions Asked in CAT exam
- Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been
- CAT - 2024
- Time and Work
- Gopi marks a price on a product in order to make 20% profit. Ravi gets 10% discount on this marked price, and thus saves Rs 15. Then, the profit, in rupees, made by Gopi by selling the product to Ravi, is
- CAT - 2024
- Profit and Loss
- Sam can complete a job in 20 days when working alone. Mohit is twice as fast as Sam and thrice as fast as Ayana in the same job. They undertake a job with an arrangement where Sam and Mohit work together on the first day, Sam and Ayana on the second day, Mohit and Ayana on the third day, and this three-day pattern is repeated till the work gets completed. Then, the fraction of total work done by Sam is
- CAT - 2024
- Time and Work
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems
- A certain amount of water was poured into a 300 litre container and the remaining portion of the container was filled with milk. Then an amount of this solution was taken out from the container which was twice the volume of water that was earlier poured into it, and water was poured to refill the container again. If the resulting solution contains 72% milk, then the amount of water, in litres, that was initially poured into the container was
- CAT - 2024
- Mixtures and Allegations
View More Questions