Solve for x 8^(2x-2)=4^x

$8^{2 x - 2} = 4^{x}$

Step 1

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

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

Step 2

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

$3 (2 x - 2) = 2 x$

Step 3

Solve for $x$ .

Simplify $3 (2 x - 2)$ .

Start simplifying.

$0 + 0 + 3 (2 x - 2) = 2 x$

Simplify by adding zeros.

$3 (2 x - 2) = 2 x$

Apply the distributive property.

$3 (2 x) + 3 \cdot - 2 = 2 x$

Multiply.

Multiply $2$ by $3$ .

$6 x + 3 \cdot - 2 = 2 x$

Multiply $3$ by $- 2$ .

$6 x - 6 = 2 x$

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$6 x - 6 - 2 x = 0$

Subtract $2 x$ from $6 x$ .

$4 x - 6 = 0$

Add $6$ to both sides of the equation.

$4 x = 6$

Divide each term in $4 x = 6$ by $4$ and simplify.

Divide each term in $4 x = 6$ by $4$ .

$\frac{4 x}{4} = \frac{6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{6}{4}$

Divide $x$ by $1$ .

$x = \frac{6}{4}$

Simplify the right side.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

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

Solve for x 8^(2x-2)=4^x

Related Questions

Support LCMGCF.com by disabling your adblocker.