Evaluate Using the Given Value 3 , 125=5^(-10+3x)

$3$ , $125 = 5^{- 10 + 3 x}$

Rewrite the equation as $5^{- 10 + 3 x} = 125$ .

$5^{- 10 + 3 x} = 125$

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

$5^{- 10 + 3 x} = 5^{3}$

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

$- 10 + 3 x = 3$

Solve for $x$ .

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

Add $10$ to both sides of the equation.

$3 x = 3 + 10$

Add $3$ and $10$ .

$3 x = 13$

Divide each term in $3 x = 13$ by $3$ and simplify.

Divide each term in $3 x = 13$ by $3$ .

$\frac{3 x}{3} = \frac{13}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{13}{3}$

Divide $x$ by $1$ .

$x = \frac{13}{3}$

Replace the variable $x$ with $\frac{13}{3}$ in the expression.

$3$