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UPTET Paper 1 2016 Solved Paper

Question : 100 of 150

Marks: +1, -0

If 9^{2x - 1} = 2^{5} - 5, then value of x is

Solution:

Concept:

Use laws of exponents to equate powers when bases are same. Convert all terms to powers of 3.

Explanation:

First, simplify the right side:

2^5 - 5 = 32 - 5 = 27

Now

27 = 3^3

. Write

9^{2x-1}

(3^2)^{2x-1} = 3^{4x-2}

Set exponents equal:

4x - 2 = 3

Solve:

4x = 5

, so

x = \frac{5}{4}

Answer:

x = \frac{5}{4}

(Option D)

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