CAT 2017 Surds and Indices Question (Hard)

Question

If , then is

Accepted Answer

Step 1 Given equation --- Step 2 Convert all terms to powers of prime factors 2 and 3 , so , so Rewrite equation --- Step 3 Simplify terms Left side Right side Bring like terms together --- Step 4 Combine coefficients Left side Right side Equation becomes --- Step 5 Cross multiply Simplify Take log

CAT 2017

Quantitative

Surds and Indices

Hard

If $9^{x - \frac{1}{2}} - 2^{2x - 2} = 4^{x - 3} \times 2^{2x - 3}$ , then $x$ is

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