CAT 2024 Surds and Indices Question (Medium)

Question

The sum of all distinct real values of that satisfy the equation , is

Accepted Answer

Step 1 Let Equation becomes y y 2 --- Step 2 Multiply through by to eliminate denominator 2y 2 8 17y 2y 2 - 17y 8 0 --- Step 3 Factorize 2y - 1 y - 8 0 Thus or . --- Step 4 Back-substitute Case 1 x log_ 10 8 log_ 10 2 3 3 log_ 10 2 Case 2 x log_ 10 2 -1 - log_ 10 2 --- Step 5 Sum of possible values

CAT 2024

Quantitative

Surds and Indices

Medium

The sum of all distinct real values of $x$ that satisfy the equation $10^x + \frac{4}{10^x} = \frac{81}{2}$ , is

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