Solve for x 1.5(4)^(2x)=12

$1.5 {(4)}^{2 x} = 12$

Divide each term in $(1.5 \cdot 4^{2 x}) = 12$ by $1.5$ and simplify.

Divide each term in $(1.5 \cdot 4^{2 x}) = 12$ by $1.5$ .

$\frac{(1.5 \cdot 4^{2 x})}{1.5} = \frac{12}{1.5}$

Simplify the left side.

Cancel the common factor of $1.5$ .

Cancel the common factor.

$\frac{1.5 \cdot 4^{2 x}}{1.5} = \frac{12}{1.5}$

Divide $4^{2 x}$ by $1$ .

$4^{2 x} = \frac{12}{1.5}$

Simplify the right side.

Divide $12$ by $1.5$ .

$4^{2 x} = 8$

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

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

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

$2 (2 x) = 3$

Solve for $x$ .

Multiply $2$ by $2$ .

$4 \cdot x = 3$

Divide each term in $(4 \cdot x) = 3$ by $4$ and simplify.

Divide each term in $(4 \cdot x) = 3$ by $4$ .

$\frac{(4 \cdot x)}{4} = \frac{3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 \cdot x}{4} = \frac{3}{4}$

Divide $x$ by $1$ .

$x = \frac{3}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}$

Decimal Form:

$x = 0.75$