Solve for x 86=9(5)^x+41

$86 = 9 {(5)}^{x} + 41$

Step 1

Rewrite the equation as $9 \cdot 5^{x} + 41 = 86$ .

$9 \cdot 5^{x} + 41 = 86$

Step 2

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

Subtract $41$ from both sides of the equation.

$9 \cdot 5^{x} = 86 - 41$

Subtract $41$ from $86$ .

$9 \cdot 5^{x} = 45$

Step 3

Divide each term in $(9 \cdot 5^{x}) = 45$ by $9$ and simplify.

Divide each term in $(9 \cdot 5^{x}) = 45$ by $9$ .

$\frac{(9 \cdot 5^{x})}{9} = \frac{45}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 \cdot 5^{x}}{9} = \frac{45}{9}$

Divide $5^{x}$ by $1$ .

$5^{x} = \frac{45}{9}$

Simplify the right side.

Divide $45$ by $9$ .

$5^{x} = 5$

Step 4

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

$5^{x} = 5^{1}$

Step 5

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

$x = 1$