Solve for x Solve 64^x=16^(x-1)

Solve $64^{x} = 16^{x - 1}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$4^{3 x} = 4^{2 (x - 1)}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$3 x = 2 (x - 1)$

Step 3

Solve for $x$ .

Simplify $2 (x - 1)$ .

Apply the distributive property.

$3 x = 2 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$3 x = 2 x - 2$

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$3 x - 2 x = - 2$

Subtract $2 x$ from $3 x$ .

$x = - 2$