CAT 2021 Logarithms Question (Hard)

Question

For a real number , if then must lie in the range

Accepted Answer

Step 1 Given Let Let Then Multiply both sides by Rewriting Add to both sides Left side can be factored as Step 2 Now express and using change of base Substitute into the expression and solve for such that From calculation This condition is satisfied when is between and , which is and Final Answer li

CAT 2021

Quantitative

Logarithms

Hard

For a real number $a$ , if $\frac{\log_{15} a + \log_{32} a}{(\log_{15} a)(\log_{32} a)} = 4$ then $a$ must lie in the range

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