Solve for x 3^(5x)=81^(x+1)

$3^{5 x} = 81^{x + 1}$

Step 1

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

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

Step 2

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

$5 x = 4 (x + 1)$

Step 3

Solve for $x$ .

Simplify $4 (x + 1)$ .

Apply the distributive property.

$5 x = 4 x + 4 \cdot 1$

Multiply $4$ by $1$ .

$5 x = 4 x + 4$

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

Subtract $4 x$ from both sides of the equation.

$5 x - 4 x = 4$

Subtract $4 x$ from $5 x$ .

$x = 4$