CAT 2024 Logarithms Question (Hard)

Question

Consider the equation log_5 x - 2 2 log_ 25 2x - 4 , where x is a real number. For how many different values of x does the given equation hold?

Optima Learn · Accepted Answer

Domain For the logs to be defined, we need and , so . Simplify the equation log_5 x-2 2 log_ 25 2x-4 . Use , so 2 log_ 25 2x-4 2 cdot 2 log_5 2x-4 . Thus the equation becomes log_5 x-2 log_5 2x-4 . Since both arguments must be positive already ensured by , we can equate x-2 2x-4 implies x 2. But vio

CAT 2024 Logarithms — Previous Year Question

CAT 2024

Quantitative

Logarithms

Hard

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