Solve 5^17x=23

$$5 ^ { 17 x } = 23$$

Solve for x

$$x=\frac{\log_{5}\left(23\right)}{17}\approx 0.114599535$$

Steps Using Definition of Logarithm

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

$$5^{17x}=23$$

Take the logarithm of both sides of the equation.

$$\log(5^{17x})=\log(23)$$

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

$$17x\log(5)=\log(23)$$

Divide both sides by \log(5).

$$17x=\frac{\log(23)}{\log(5)}$$

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

$$17x=\log_{5}\left(23\right)$$

Divide both sides by 17.

$$x=\frac{\log_{5}\left(23\right)}{17}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{17\ln(5)}+\frac{\log_{5}\left(23\right)}{17}$$

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