Solve (1.18)^x-1/18=20

$$\frac { ( 1.18 ) ^ { x } - 1 } { 18 } = 20$$

Solve for x

$$x=2\log_{1.18}\left(19\right)\approx 35.579240171$$

Steps Using Definition of Logarithm

Multiply both sides by 18.

$$1.18^{x}-1=20\times 18$$

Multiply 20 and 18 to get 360.

$$1.18^{x}-1=360$$

Add 1 to both sides of the equation.

$$1.18^{x}=361$$

Take the logarithm of both sides of the equation.

$$\log(1.18^{x})=\log(361)$$

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

$$x\log(1.18)=\log(361)$$

Divide both sides by \log(1.18).

$$x=\frac{\log(361)}{\log(1.18)}$$

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

$$x=\log_{1.18}\left(361\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.18)}+2\log_{1.18}\left(19\right)$$

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