Solve 6^22x-3=1

$${ 6 }^{ 22x-3 } =1$$

Solve for x

$$x=\frac{3}{22}\approx 0.136363636$$

Steps Using Definition of Logarithm

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

$$6^{22x-3}=1$$

Take the logarithm of both sides of the equation.

$$\log(6^{22x-3})=\log(1)$$

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

$$\left(22x-3\right)\log(6)=\log(1)$$

Divide both sides by \log(6).

$$22x-3=\frac{\log(1)}{\log(6)}$$

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

$$22x-3=\log_{6}\left(1\right)$$

Add 3 to both sides of the equation.

$$22x=-\left(-3\right)$$

Divide both sides by 22.

$$x=\frac{3}{22}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{11\ln(6)}+\frac{3}{22}$$

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