Solve 1.18^x-1/.18=20

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

Solve for x

$$x=\log_{1.18}\left(4.6\right)\approx 9.220079635$$

Steps Using Definition of Logarithm

Multiply both sides by 0.18.

$$1.18^{x}-1=20\times 0.18$$

Multiply 20 and 0.18 to get 3.6.

$$1.18^{x}-1=3.6$$

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

$$1.18^{x}-1=\frac{18}{5}$$

Add 1 to both sides of the equation.

$$1.18^{x}=\frac{23}{5}$$

Take the logarithm of both sides of the equation.

$$\log(1.18^{x})=\log(\frac{23}{5})$$

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

$$x\log(1.18)=\log(\frac{23}{5})$$

Divide both sides by \log(1.18).

$$x=\frac{\log(\frac{23}{5})}{\log(1.18)}$$

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

$$x=\log_{1.18}\left(\frac{23}{5}\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(1.18)}+\log_{1.18}\left(4.6\right)$$

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