CAT 2023 Logarithms Question (Hard)

Question

For some positive real number , if , then the value of is

Accepted Answer

Step 1 Given equation log_ x 0.008 3 --- Step 2 Express as power of 5 0.008 1000 10 3 5 -3 --- Step 3 Simplify log_ x 5 -3 3 log_ x 5 2 3 3 log_ x 5 5 3 --- Step 4 Solve for log_ x 6 --- Step 5 Convert back to x 6 3 2 3 3 27 --- Step 6 Compute 3x 2 3 times 27 2 3 times 729 2187 3 7 --- Step 7 Logari

CAT 2023

Quantitative

Logarithms

Hard

For some positive real number $x$ , if $\log_{\sqrt{3}}(x) + \frac{\log_x(25)}{\log_x(0.008)} = \frac{16}{3}$ , then the value of $\log_3\left(3 x^2\right)$ is

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