Solve for x 36^x=6

$36^{x} = 6$

Step 1

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

$6^{2 x} = 6^{1}$

Step 2

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

$2 x = 1$

Step 3

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$