Find All Complex Solutions 81^x=3

$81^{x} = 3$

Step 1

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

$3^{4 x} = 3^{1}$

Step 2

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

$4 x = 1$

Step 3

Divide each term in $4 x = 1$ by $4$ and simplify.

Divide each term in $4 x = 1$ by $4$ .

$\frac{4 x}{4} = \frac{1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Divide $x$ by $1$ .

$x = \frac{1}{4}$