# CAT Practice : Exponents and Logarithms

Its amazing how many questions one can solve in the exam knowing only the very basics.

## Logarithm - Simple

Q.2: log9 (3log2 (1 + log3 (1 + 2log2x))) = ${1 \over 2}$. Find x.
1. 4
2. ${1 \over 2}$
3. 1
4. 2

Choice D. 2

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## Detailed Solution

log9 (3log2 (1 + log3 (1 + 2log2x)) = ${1 \over 2}$
3log2(1 + log3(1 + 2log2x)) = 91/2 = 3
log2(1 + log3(1 + 2log2x) = 1
1 + log3(1 + 2log2x) = 2
log3(1 + 2log2x) = 1
1 + 2log2x = 3
2log2x = 2
log2x = 1
x = 2

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