CAT 2017 Logarithms Question (Medium)

Question

If is a real number such that , then which of the following is true?

Accepted Answer

Step 1 We are given log_ 3 5 log_ 5 2 x Apply the change of base formula log_ 3 5 log 3 , quad log_ 5 2 x log 5 So the equation becomes log 3 log 5 Step 2 Cross-multiply log 5 2 log 3 cdot log 2 x Solve for log 2 x log 3 Use approximations log 5 approx 0.6990, quad log 3 approx 0.4771 log 2 x approx

CAT 2017

Quantitative

Logarithms

Medium

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

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