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

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

Step 1

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

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

Step 2

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

$4 x + 1 = 3$

Step 3

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$4 x = 3 - 1$

Subtract $1$ from $3$ .

$4 x = 2$

Divide each term in $4 x = 2$ by $4$ and simplify.

Divide each term in $4 x = 2$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4}$

Divide $x$ by $1$ .

$x = \frac{2}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$