Solve 27*3^n+2=243

$$27 \times 3 ^ { n + 2 } = 243$$

Solve for n

$$n=0$$

Steps Using Definition of Logarithm

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

$$27\times 3^{n+2}=243$$

Divide both sides by 27.

$$3^{n+2}=9$$

Take the logarithm of both sides of the equation.

$$\log(3^{n+2})=\log(9)$$

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

$$\left(n+2\right)\log(3)=\log(9)$$

Divide both sides by \log(3).

$$n+2=\frac{\log(9)}{\log(3)}$$

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

$$n+2=\log_{3}\left(9\right)$$

Subtract 2 from both sides of the equation.

$$n=2-2$$