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Question : 1 of 86

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Simplification of

9^{x+3}=27^{x-1}

gives

8
7
9
None

Solution:

Concept:

Express both sides with same base and equate exponents.

Explanation:

Rewrite

9

and

27

as powers of

3

:

9 = 3^2

,

27 = 3^3

.

Thus

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

and

27^{x-1} = (3^3)^{x-1} = 3^{3(x-1)}

.

Since bases are equal, equate exponents:

2(x+3) = 3(x-1)

.

Expand:

2x + 6 = 3x - 3

.

Bring terms:

6 + 3 = 3x - 2x

gives

9 = x

.

Answer:

x = 9

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