Solve for x 3125=5^(-10+3x)

$3125 = 5^{- 10 + 3 x}$

Step 1

Rewrite the equation as $5^{- 10 + 3 x} = 3125$ .

$5^{- 10 + 3 x} = 3125$

Step 2

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

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

Step 3

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

$- 10 + 3 x = 5$

Step 4

Solve for $x$ .

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

Add $10$ to both sides of the equation.

$3 x = 5 + 10$

Add $5$ and $10$ .

$3 x = 15$

Divide each term in $3 x = 15$ by $3$ and simplify.

Divide each term in $3 x = 15$ by $3$ .

$\frac{3 x}{3} = \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{15}{3}$

Divide $x$ by $1$ .

$x = \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$x = 5$