Solve (3^y-10)=10

$$( 3 ^ { y } - 10 ) = 10$$

Solve for y

$$y=\log_{3}\left(20\right)\approx 2.726833028$$

Steps Using Definition of Logarithm

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

$$3^{y}-10=10$$

Add 10 to both sides of the equation.

$$3^{y}=20$$

Take the logarithm of both sides of the equation.

$$\log(3^{y})=\log(20)$$

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

$$y\log(3)=\log(20)$$

Divide both sides by \log(3).

$$y=\frac{\log(20)}{\log(3)}$$

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

$$y=\log_{3}\left(20\right)$$

Solve for y (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(3)}+\log_{3}\left(20\right)$$

$$n_{1}\in \mathrm{Z}$$