Solve for x 5^(4x+1)=25

$5^{4 x + 1} = 25$

Step 1

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

$5^{4 x + 1} = 5^{2}$

Step 2

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

$4 x + 1 = 2$

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.

$4 x = 2 - 1$

Subtract $1$ from $2$ .

$4 x = 1$

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 $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.25$