Solve 103^x=15

$$103 ^ { x } = 15$$

Solve for x

$$x=\log_{103}\left(15\right)\approx 0.584295265$$

Steps Using Definition of Logarithm

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

$$103^{x}=15$$

Take the logarithm of both sides of the equation.

$$\log(103^{x})=\log(15)$$

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

$$x\log(103)=\log(15)$$

Divide both sides by \log(103).

$$x=\frac{\log(15)}{\log(103)}$$

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

$$x=\log_{103}\left(15\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(103)}+\log_{103}\left(15\right)$$

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