Solve for x 3^(4x)=1/27

$3^{4 x} = \frac{1}{27}$

Step 1

Raise $27$ to the power of $1$ .

$3^{4 x} = \frac{1}{27^{1}}$

Step 2

Move $27^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{4 x} = 27^{- 1}$

Step 3

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

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

Step 4

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

$4 x = - 3$

Step 5

Divide each term in $4 x = - 3$ by $4$ and simplify.

Divide each term in $4 x = - 3$ by $4$ .

$\frac{4 x}{4} = \frac{- 3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 3}{4}$

Divide $x$ by $1$ .

$x = \frac{- 3}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{4}$

Decimal Form:

$x = - 0.75$