Solve for x 5^(4x-7)=125

$5^{4 x - 7} = 125$

Step 1

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

$5^{4 x - 7} = 5^{3}$

Step 2

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

$4 x - 7 = 3$

Step 3

Solve for $x$ .

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

Add $7$ to both sides of the equation.

$4 x = 3 + 7$

Add $3$ and $7$ .

$4 x = 10$

Divide each term in $4 x = 10$ by $4$ and simplify.

Divide each term in $4 x = 10$ by $4$ .

$\frac{4 x}{4} = \frac{10}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{10}{4}$

Divide $x$ by $1$ .

$x = \frac{10}{4}$

Simplify the right side.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{2}$

Decimal Form:

$x = 2.5$

Mixed Number Form:

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