Solve 9^n+2=240+9

$$9 ^ { n + 2 } = 240 + 9$$

Solve for n

$$n=\frac{\log_{3}\left(249\right)-4}{2}\approx 0.511101029$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$9^{n+2}=249$$

Take the logarithm of both sides of the equation.

$$\log(9^{n+2})=\log(249)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$\left(n+2\right)\log(9)=\log(249)$$

Divide both sides by \log(9).

$$n+2=\frac{\log(249)}{\log(9)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$n+2=\log_{9}\left(249\right)$$

Subtract 2 from both sides of the equation.

$$n=\frac{\log_{3}\left(249\right)}{2}-2$$