Solve for x 6^((x-3)/4) = square root of 6

$6^{\frac{x - 3}{4}} = \sqrt{6}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$6^{\frac{x - 3}{4}} = 6^{\frac{1}{2}}$

Step 2

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

$\frac{x - 3}{4} = \frac{1}{2}$

Step 3

Solve for $x$ .

Multiply both sides of the equation by $4$ .

$4 \frac{x - 3}{4} = 4 (\frac{1}{2})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x - 3}{4} = 4 (\frac{1}{2})$

Rewrite the expression.

$x - 3 = 4 (\frac{1}{2})$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x - 3 = 2 (2) \frac{1}{2}$

Cancel the common factor.

$x - 3 = 2 \cdot 2 \frac{1}{2}$

Rewrite the expression.

$x - 3 = 2$

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

Add $3$ to both sides of the equation.

$x = 2 + 3$

Add $2$ and $3$ .

$x = 5$