Solve 3^n-2=19-10

$$3 ^ { n - 2 } = 19 - 10$$

Solve for n

$$n=4$$

Steps Using Definition of Logarithm

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

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

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).

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

Add 2 to both sides of the equation.

$$n=2-\left(-2\right)$$