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CAT 2017 Slot 2 QA Question & Solution

AlgebraMedium

Question

If x is a real number such that $\log_{3}5= \log_{5}(2 + x)$, then which of the following is true?

Options

0 < x < 3
23 < x < 30
x > 30
3 < x < 23

Solution

$1 < \log_{3}5 < 2$
=> $1 < \log_{5}(2 + x) < 2$
=> $5 < 2 + x < 25$
=> $3 < x < 23$