Solve for x 1/125=25^(5x-3)

$\frac{1}{125} = 25^{5 x - 3}$

Step 1

Rewrite the equation as $25^{5 x - 3} = \frac{1}{125}$ .

$25^{5 x - 3} = \frac{1}{125}$

Step 2

Raise $125$ to the power of $1$ .

$25^{5 x - 3} = \frac{1}{125^{1}}$

Step 3

Move $125^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$25^{5 x - 3} = 125^{- 1}$

Step 4

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

$5^{2 (5 x - 3)} = 5^{- 3}$

Step 5

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

$2 (5 x - 3) = - 3$

Step 6

Solve for $x$ .

Divide each term in $2 (5 x - 3) = - 3$ by $2$ and simplify.

Divide each term in $2 (5 x - 3) = - 3$ by $2$ .

$\frac{2 (5 x - 3)}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (5 x - 3)}{2} = \frac{- 3}{2}$

Divide $5 x - 3$ by $1$ .

$5 x - 3 = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$5 x - 3 = - \frac{3}{2}$

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

Add $3$ to both sides of the equation.

$5 x = - \frac{3}{2} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 x = - \frac{3}{2} + 3 \cdot \frac{2}{2}$

Combine $3$ and $\frac{2}{2}$ .

$5 x = - \frac{3}{2} + \frac{3 \cdot 2}{2}$

Combine the numerators over the common denominator.

$5 x = \frac{- 3 + 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $3$ by $2$ .

$5 x = \frac{- 3 + 6}{2}$

Add $- 3$ and $6$ .

$5 x = \frac{3}{2}$

Divide each term in $5 x = \frac{3}{2}$ by $5$ and simplify.

Divide each term in $5 x = \frac{3}{2}$ by $5$ .

$\frac{5 x}{5} = \frac{\frac{3}{2}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{\frac{3}{2}}{5}$

Divide $x$ by $1$ .

$x = \frac{\frac{3}{2}}{5}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{3}{2} \cdot \frac{1}{5}$

Multiply $\frac{3}{2} \cdot \frac{1}{5}$ .

Multiply $\frac{3}{2}$ by $\frac{1}{5}$ .

$x = \frac{3}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{3}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{10}$

Decimal Form:

$x = 0.3$

Solve for x 1/125=25^(5x-3)

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