Solve 5^y-3=125

$$5 ^ { y - 3 } = 125$$

Solve for y

$$y=6$$

Steps Using Definition of Logarithm

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

$$5^{y-3}=125$$

Take the logarithm of both sides of the equation.

$$\log(5^{y-3})=\log(125)$$

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

$$\left(y-3\right)\log(5)=\log(125)$$

Divide both sides by \log(5).

$$y-3=\frac{\log(125)}{\log(5)}$$

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

$$y-3=\log_{5}\left(125\right)$$

Add 3 to both sides of the equation.

$$y=3-\left(-3\right)$$

Solve for y (complex solution)

$$y=\frac{i\times 2\pi n_{1}}{\ln(5)}+6$$

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