Solve 15^3y=3

$$15 ^ { 3 y } = 3$$

Solve for y

$$y=\frac{\log_{15}\left(3\right)}{3}\approx 0.135227957$$

Steps Using Definition of Logarithm

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

$$15^{3y}=3$$

Take the logarithm of both sides of the equation.

$$\log(15^{3y})=\log(3)$$

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

$$3y\log(15)=\log(3)$$

Divide both sides by \log(15).

$$3y=\frac{\log(3)}{\log(15)}$$

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

$$3y=\log_{15}\left(3\right)$$

Divide both sides by 3.

$$y=\frac{\log_{15}\left(3\right)}{3}$$

Solve for y (complex solution)

$$y=\frac{2\pi n_{1}i}{3\ln(15)}+\frac{\log_{15}\left(3\right)}{3}$$

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