Solve for x 4^(2x)+1=17

$4^{2 x} + 1 = 17$

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

Subtract $1$ from both sides of the equation.

$4^{2 x} = 17 - 1$

Subtract $1$ from $17$ .

$4^{2 x} = 16$

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

$4^{2 x} = 4^{2}$

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

$2 x = 2$

Divide each term in $2 x = 2$ by $2$ and simplify.

Divide each term in $2 x = 2$ by $2$ .

$\frac{2 x}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{2}{2}$

Divide $x$ by $1$ .

$x = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$