Solve for x 4^x-5=3

$4^{x} - 5 = 3$

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

Add $5$ to both sides of the equation.

$4^{x} = 3 + 5$

Add $3$ and $5$ .

$4^{x} = 8$

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

$2^{2 x} = 2^{3}$

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

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$