If 3^{2x - 1} = 27, what is the value of x? — ACT

If $3^{2x - 1} = 27$ , what is the value of $x$ ?

Answer: 2

The value of

x

2

Rewriting

27

3^3

gives the equation

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

. Equating the exponents yields

2x - 1 = 3

, which solves to

x = 2

Rewrite the right side of the equation with a base of

3

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

Expressing both sides of the equation with a common base allows for direct comparison of the exponents.

Set the exponents equal to each other.

2x - 1 = 3

Since the bases are both

3

, their exponents must be equal for the expressions to be equal.

Solve the linear equation for

x

x = 2

Adding

1

to both sides gives

2x = 4

. Dividing both sides by

2

results in

x = 2

Solving exponential equations by expressing both sides with a common base

Question