CAT 2017 Surds and Indices Question (Medium)

Question

If , then is

Accepted Answer

Step 1 Express all terms in base 3 Since and 9 2x - 1 3 2 2x - 1 3 4x - 2 81 x - 1 3 4 x - 1 3 4x - 4 --- Step 2 Substitute back into the equation 3 4x - 2 - 3 4x - 4 1944 Take common 3 4x - 4 3 2 - 1 1944 3 4x - 4 9 - 1 1944 3 4x - 4 cdot 8 1944 --- Step 3 Solve for exponent 3 4x - 4 8 243 Rightarr

CAT 2017

Quantitative

Surds and Indices

Medium

If $9^{2x-1} - 81^{x-1} = 1944$ , then $x$ is

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