Solve for x 4^(3x-7)=16

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

Step 1

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

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

Step 2

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

$3 x - 7 = 2$

Step 3

Solve for $x$ .

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

Add $7$ to both sides of the equation.

$3 x = 2 + 7$

Add $2$ and $7$ .

$3 x = 9$

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 $3$ .

$x = 3$