Solve 3^y=25

$$3 ^ { y } = 25$$

Solve for y

$$y=2\log_{3}\left(5\right)\approx 2.929947041$$

Steps Using Definition of Logarithm

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

$$3^{y}=25$$

Take the logarithm of both sides of the equation.

$$\log(3^{y})=\log(25)$$

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

$$y\log(3)=\log(25)$$

Divide both sides by \log(3).

$$y=\frac{\log(25)}{\log(3)}$$

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

$$y=\log_{3}\left(25\right)$$

Solve for y (complex solution)

$$y=\frac{2\pi n_{1}i}{\ln(3)}+2\log_{3}\left(5\right)$$

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