Question

Difficulty: EasyIndices and Laws of Indices

If $2^{3x - 1} = 32$ , find the value of $x$ .

Answer: 2

The value of

x

is 2.

Rewriting 32 as

2^5

allows equating the exponents

3x - 1 = 5

. Solving for

x

gives

3x = 6

, which simplifies to

x = 2

Express both sides of the equation using a common base of 2

2^{3x - 1} = 2^5

The number 32 can be rewritten in index form as

2^5

Equate the indices

3x - 1 = 5

a^m = a^n

for a non-zero base

a \neq 1

, then

m = n

Solve the linear equation for

x

x = 2

Adding 1 to both sides yields

3x = 6

, and dividing by 3 gives

x = 2

Solving exponential equations by expressing numbers with equal bases

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