Solve for x 8^7=8^3*8^x

$8^{7} = 8^{3} \cdot 8^{x}$

Step 1

Rewrite the equation as $8^{3} \cdot 8^{x} = 8^{7}$ .

$8^{3} \cdot 8^{x} = 8^{7}$

Step 2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 3

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

$3 + x = 7$

Step 4

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

Subtract $3$ from both sides of the equation.

$x = 7 - 3$

Subtract $3$ from $7$ .

$x = 4$