Solve for x 5^(4x)=125^(x+1)

$5^{4 x} = 125^{x + 1}$

Step 1

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

$5^{4 x} = 5^{3 (x + 1)}$

Step 2

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

$4 x = 3 (x + 1)$

Step 3

Solve for $x$ .

Simplify $3 (x + 1)$ .

Apply the distributive property.

$4 x = 3 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$4 x = 3 x + 3$

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

Subtract $3 x$ from both sides of the equation.

$4 x - 3 x = 3$

Subtract $3 x$ from $4 x$ .

$x = 3$