Solve for x (13^5)/(13^x)=13^4

$\frac{13^{5}}{13^{x}} = 13^{4}$

Step 1

Move $13^{x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$13^{5} \cdot 13^{- x} = 13^{4}$

Step 2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$13^{5 - x} = 13^{4}$

Step 3

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

$5 - x = 4$

Step 4

Solve for $x$ .

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

Subtract $5$ from both sides of the equation.

$- x = 4 - 5$

Subtract $5$ from $4$ .

$- x = - 1$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x = 1$