If 5^a=9^b=2025, then the value of \frac{a b}{a+b}=

CMAT Exam 2023 Shift 2 Solved Paper

Question : 19 of 100

Marks: +1, -0

5^a=9^b=2025

, then the value of

\;{a b}/{a+b}=

Solution:

It is given,

\;5^a=9^b=2025

\;5^a=2025

Applying log on both the sides, we get

\;\log _5 5^a=\log _5 2045

\;a=\log _5 2045

Similarly, we get

b=\log _9 2045

\;\;{a b}/{a+b}=\;{1}/{{1}/{a}+\;{1}/{b}}

\;\;{1}/{a}=\log _{2045} 5

\;\;{1}/{b}=\log _{2045} 9

\;\;{1}/{a}+\;{1}/{b}=\log _{2045} 45

\;\;{a b}/{a+b}=\log _{45} 2045=2

The answer is option C.

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