Solve 9²x + 1} = 81³x + 2}

Correct Answer is : −34\; -3/44−3

Correct Answer is : −34\; -3/44−3

Test Index

WAEC Further Mathematics 2011 Paper

Question : 16

Total: 40

Solve

9^{2x + 1} = 81^{3x + 2}

Solution:

Concept:

Express both sides with the same base, then equate the exponents.

Explanation:

Rewrite

81

9^2

So,

81^{3x+2} = (9^2)^{3x+2}

Using the power rule,

(9^2)^{3x+2} = 9^{6x+4}

Thus,

9^{2x+1} = 9^{6x+4}

Since the bases are equal, equate the powers:

2x + 1 = 6x + 4

Rearrange:

1 - 4 = 6x - 2x

So,

-3 = 4x

Therefore,

x = \frac{-3}{4}

Answer:

x = \frac{-3}{4}

, which is option A.

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