Solve 12^6*12^4=12^y

$$12 ^ { 6 } \times 12 ^ { 4 } = 12 ^ { y }$$

Solve for y

$$y=10$$

Steps Using Definition of Logarithm

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$12^{10}=12^{y}$$

Calculate 12 to the power of 10 and get 61917364224.

$$61917364224=12^{y}$$

Swap sides so that all variable terms are on the left hand side.

$$12^{y}=61917364224$$

Take the logarithm of both sides of the equation.

$$\log(12^{y})=\log(61917364224)$$

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

$$y\log(12)=\log(61917364224)$$

Divide both sides by \log(12).

$$y=\frac{\log(61917364224)}{\log(12)}$$

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

$$y=\log_{12}\left(61917364224\right)$$

Solve for y (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(12)}+10$$

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