Solve for x 4^(7+3x)=1/16

$4^{7 + 3 x} = \frac{1}{16}$

Step 1

Raise $16$ to the power of $1$ .

$4^{7 + 3 x} = \frac{1}{16^{1}}$

Step 2

Move $16^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$4^{7 + 3 x} = 16^{- 1}$

Step 3

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

$4^{7 + 3 x} = 4^{- 2}$

Step 4

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

$7 + 3 x = - 2$

Step 5

Solve for $x$ .

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

Subtract $7$ from both sides of the equation.

$3 x = - 2 - 7$

Subtract $7$ from $- 2$ .

$3 x = - 9$

Divide each term in $3 x = - 9$ by $3$ and simplify.

Divide each term in $3 x = - 9$ by $3$ .

$\frac{3 x}{3} = \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 9}{3}$

Divide $x$ by $1$ .

$x = \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$x = - 3$