CAT 2025 Logarithms Question (Hard)

Question

The sum of all possible real values of x for which log _ x - 3 left x 2 - 9 right log _ x - 3 x 1 2 , is

Accepted Answer

Since the base of the logarithm has to be greater than zero and cannot be 1, x has to be greater than 3 and cannot be 4. Also, since x 2-9 0, x will be greater than 3. The equation can be rewritten as log_ x-3 x 2 -9 - log_ x-3 x 1 2 Or, log_ x-3 x 1 2 Rightarrow x 1 x-3 2 Rightarrow x 1 x-3 Rightar

CAT 2025

Quantitative

Logarithms

Hard

The sum of all possible real values of ( x ) for which ( \log _ { x - 3 } \left( x ^ { 2 } - 9 \right) = \log _ { x - 3 } ( x + 1 ) + 2 ), is

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