Solve for x 6^9*6^x=6^2

$6^{9} \cdot 6^{x} = 6^{2}$

Step 1

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

$6^{9 + x} = 6^{2}$

Step 2

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

$9 + x = 2$

Step 3

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

Subtract $9$ from both sides of the equation.

$x = 2 - 9$

Subtract $9$ from $2$ .

$x = - 7$