Solve for x 5^(x-4)=25^(x-6)

$5^{x - 4} = 25^{x - 6}$

Step 1

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

$5^{x - 4} = 5^{2 (x - 6)}$

Step 2

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

$x - 4 = 2 (x - 6)$

Step 3

Solve for $x$ .

Simplify $2 (x - 6)$ .

Rewrite.

$x - 4 = 0 + 0 + 2 (x - 6)$

Simplify by adding zeros.

$x - 4 = 2 (x - 6)$

Apply the distributive property.

$x - 4 = 2 x + 2 \cdot - 6$

Multiply $2$ by $- 6$ .

$x - 4 = 2 x - 12$

Move all terms containing $x$ to the left side of the equation.

Subtract $2 x$ from both sides of the equation.

$x - 4 - 2 x = - 12$

Subtract $2 x$ from $x$ .

$- x - 4 = - 12$

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

Add $4$ to both sides of the equation.

$- x = - 12 + 4$

Add $- 12$ and $4$ .

$- x = - 8$

Divide each term in $- x = - 8$ by $- 1$ and simplify.

Divide each term in $- x = - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 8}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 1}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$x = 8$