Solve 12^y-6=3

$$12 ^ { y - 6 } = 3$$

Solve for y

$$y=\log_{12}\left(8957952\right)\approx 6.442114109$$

Steps Using Definition of Logarithm

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

$$12^{y-6}=3$$

Take the logarithm of both sides of the equation.

$$\log(12^{y-6})=\log(3)$$

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

$$\left(y-6\right)\log(12)=\log(3)$$

Divide both sides by \log(12).

$$y-6=\frac{\log(3)}{\log(12)}$$

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

$$y-6=\log_{12}\left(3\right)$$

Add 6 to both sides of the equation.

$$y=\log_{12}\left(3\right)-\left(-6\right)$$