Solve for x 1/32=2^(6x)

$\frac{1}{32} = 2^{6 x}$

Step 1

Rewrite the equation as $2^{6 x} = \frac{1}{32}$ .

$2^{6 x} = \frac{1}{32}$

Step 2

Raise $32$ to the power of $1$ .

$2^{6 x} = \frac{1}{32^{1}}$

Step 3

Move $32^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$2^{6 x} = 32^{- 1}$

Step 4

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

$2^{6 x} = 2^{- 5}$

Step 5

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

$6 x = - 5$

Step 6

Divide each term in $6 x = - 5$ by $6$ and simplify.

Divide each term in $6 x = - 5$ by $6$ .

$\frac{6 x}{6} = \frac{- 5}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 5}{6}$

Divide $x$ by $1$ .

$x = \frac{- 5}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{6}$

Decimal Form:

$x = - 0.8\overline{3}$