Evaluate 7^(x-5)=49^x

$7^{x - 5} = 49^{x}$

Step 1

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

$7^{x - 5} = 7^{2 x}$

Step 2

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

$x - 5 = 2 x$

Step 3

Solve for $x$ .

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

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

$x - 5 - 2 x = 0$

Subtract $2 x$ from $x$ .

$- x - 5 = 0$

Add $5$ to both sides of the equation.

$- x = 5$

Divide each term in $- x = 5$ by $- 1$ and simplify.

Divide each term in $- x = 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{5}{- 1}$

Simplify the right side.

Divide $5$ by $- 1$ .

$x = - 5$