Solve 13122=18*3^x-1

$$13122 = 18 \times { 3 }^{ x-1 }$$

Solve for x

$$x=7$$

Steps Using Definition of Logarithm

Divide both sides by 18.

$$\frac{13122}{18}=3^{x-1}$$

Divide 13122 by 18 to get 729.

$$729=3^{x-1}$$

Swap sides so that all variable terms are on the left hand side.

$$3^{x-1}=729$$

Take the logarithm of both sides of the equation.

$$\log(3^{x-1})=\log(729)$$

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

$$\left(x-1\right)\log(3)=\log(729)$$

Divide both sides by \log(3).

$$x-1=\frac{\log(729)}{\log(3)}$$

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

$$x-1=\log_{3}\left(729\right)$$

Add 1 to both sides of the equation.

$$x=6-\left(-1\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(3)}+7$$

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