CAT 2020 Logarithms Question (Hard)

Question

Let , and , then equals

Accepted Answer

Step 1 Given data log_a 30 A quad log_a 3 -B quad Also given log_2 a 3 implies log_a 2 3 --- Step 2 Convert equations to base 2 Divide Equation 1 and 2 by log_2 30 3 log_2 3 - 3 --- Step 3 Expand log_2 30 log_2 5 times 3 times 2 3 log_2 5 log_2 3 log_2 2 3 log_2 5 log_2 3 1 quad --- Step 4 Expand lo

CAT 2020

Quantitative

Logarithms

Hard

Let $\log_a 30 = A$ , $\log_a \frac{5}{3} = -B$ and $\log_2 a = \frac{1}{3}$ , then $\log_3 a$ equals

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