Evaluate 3^(9x)=3^(7x+8)

$3^{9 x} = 3^{7 x + 8}$

Step 1

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

$3^{9 x} = 3^{7 x + 8}$

Step 2

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

$9 x = 7 x + 8$

Step 3

Solve for $x$ .

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

Subtract $7 x$ from both sides of the equation.

$9 x - 7 x = 8$

Subtract $7 x$ from $9 x$ .

$2 x = 8$

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$