Solve for x 3^(2x-5)=9

$3^{2 x - 5} = 9$

Step 1

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

$3^{2 x - 5} = 3^{2}$

Step 2

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

$2 x - 5 = 2$

Step 3

Solve for $x$ .

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

Add $5$ to both sides of the equation.

$2 x = 2 + 5$

Add $2$ and $5$ .

$2 x = 7$

Divide each term in $2 x = 7$ by $2$ and simplify.

Divide each term in $2 x = 7$ by $2$ .

$\frac{2 x}{2} = \frac{7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{7}{2}$

Divide $x$ by $1$ .

$x = \frac{7}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{2}$

Decimal Form:

$x = 3.5$

Mixed Number Form:

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