Solve for x 2^(7x-8)=64

$2^{7 x - 8} = 64$

Step 1

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

$2^{7 x - 8} = 2^{6}$

Step 2

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

$7 x - 8 = 6$

Step 3

Solve for $x$ .

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

Add $8$ to both sides of the equation.

$7 x = 6 + 8$

Add $6$ and $8$ .

$7 x = 14$

Divide each term in $7 x = 14$ by $7$ and simplify.

Divide each term in $7 x = 14$ by $7$ .

$\frac{7 x}{7} = \frac{14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{14}{7}$

Divide $x$ by $1$ .

$x = \frac{14}{7}$

Simplify the right side.

Divide $14$ by $7$ .

$x = 2$