Solve for x 3^(4x+5)=81^(-3/4)

$3^{4 x + 5} = 81^{- \frac{3}{4}}$

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

$3^{4 x + 5} = 3^{4 (- \frac{3}{4})}$

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

$4 x + 5 = 4 (- \frac{3}{4})$

Solve for $x$ .

Simplify $4 (- \frac{3}{4})$ .

Rewrite.

$4 x + 5 = 0 + 0 + 4 (- \frac{3}{4})$

Simplify by adding zeros.

$4 x + 5 = 4 (- \frac{3}{4})$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$4 x + 5 = 4 (\frac{- 3}{4})$

Cancel the common factor.

$4 x + 5 = 4 (\frac{- 3}{4})$

Rewrite the expression.

$4 x + 5 = - 3$

Move all terms not containing $x$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$4 x = - 3 - 5$

Subtract $5$ from $- 3$ .

$4 x = - 8$

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$