Solve for x 32^(2x-3)=2

$32^{2 x - 3} = 2$

Step 1

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

$2^{5 (2 x - 3)} = 2^{1}$

Step 2

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

$5 (2 x - 3) = 1$

Step 3

Solve for $x$ .

Divide each term in $5 (2 x - 3) = 1$ by $5$ and simplify.

Divide each term in $5 (2 x - 3) = 1$ by $5$ .

$\frac{5 (2 x - 3)}{5} = \frac{1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (2 x - 3)}{5} = \frac{1}{5}$

Divide $2 x - 3$ by $1$ .

$2 x - 3 = \frac{1}{5}$

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

Add $3$ to both sides of the equation.

$2 x = \frac{1}{5} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$2 x = \frac{1}{5} + 3 \cdot \frac{5}{5}$

Combine $3$ and $\frac{5}{5}$ .

$2 x = \frac{1}{5} + \frac{3 \cdot 5}{5}$

Combine the numerators over the common denominator.

$2 x = \frac{1 + 3 \cdot 5}{5}$

Simplify the numerator.

Multiply $3$ by $5$ .

$2 x = \frac{1 + 15}{5}$

Add $1$ and $15$ .

$2 x = \frac{16}{5}$

Divide each term in $2 x = \frac{16}{5}$ by $2$ and simplify.

Divide each term in $2 x = \frac{16}{5}$ by $2$ .

$\frac{2 x}{2} = \frac{\frac{16}{5}}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{\frac{16}{5}}{2}$

Divide $x$ by $1$ .

$x = \frac{\frac{16}{5}}{2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{16}{5} \cdot \frac{1}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $16$ .

$x = \frac{2 (8)}{5} \cdot \frac{1}{2}$

Cancel the common factor.

$x = \frac{2 \cdot 8}{5} \cdot \frac{1}{2}$

Rewrite the expression.

$x = \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{8}{5}$

Decimal Form:

$x = 1.6$

Mixed Number Form:

$x = 1 \frac{3}{5}$

Solve for x 32^(2x-3)=2

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