Evaluate 9^(8x)=27

$9^{8 x} = 27$

Step 1

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

$3^{2 (8 x)} = 3^{3}$

Step 2

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

$2 (8 x) = 3$

Step 3

Solve for $x$ .

Multiply $8$ by $2$ .

$16 \cdot x = 3$

Divide each term in $(16 \cdot x) = 3$ by $16$ and simplify.

Divide each term in $(16 \cdot x) = 3$ by $16$ .

$\frac{(16 \cdot x)}{16} = \frac{3}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 \cdot x}{16} = \frac{3}{16}$

Divide $x$ by $1$ .

$x = \frac{3}{16}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{16}$

Decimal Form:

$x = 0.1875$