Solve for x 6^5=6^x*6^4

$6^{5} = 6^{x} \cdot 6^{4}$

Step 1

Rewrite the equation as $6^{x} \cdot 6^{4} = 6^{5}$ .

$6^{x} \cdot 6^{4} = 6^{5}$

Step 2

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

$6^{x + 4} = 6^{5}$

Step 3

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

$x + 4 = 5$

Step 4

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

Subtract $4$ from both sides of the equation.

$x = 5 - 4$

Subtract $4$ from $5$ .

$x = 1$