Question

Difficulty: EasySurds and Indices

If $3^{x + 2} = 81$ , what is the value of $x$ ?

Answer: 2

The value of

x

is 2.

Rewriting 81 as

3^4

gives

3^{x+2} = 3^4

. Since the bases are equal, setting the exponents equal gives

x + 2 = 4

, which solves to

x = 2

Express the right-hand side with a base of 3

81 = 3^4

Both sides must have the same base to apply the laws of indices.

Equate the exponents

x + 2 = 4

a^m = a^n

(where

a > 0

and

a \neq 1

), then

m = n

Solve for

x

x = 2

Subtracting 2 from both sides isolates

x

Equating exponents of equal bases

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