Solve 7(3)^x-20=169

$$7 ( 3 ) ^ { x } - 20 = 169$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$7\times 3^{x}-20=169$$

Add 20 to both sides of the equation.

$$7\times 3^{x}=189$$

Divide both sides by 7.

$$3^{x}=27$$

Take the logarithm of both sides of the equation.

$$\log(3^{x})=\log(27)$$

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

$$x\log(3)=\log(27)$$

Divide both sides by \log(3).

$$x=\frac{\log(27)}{\log(3)}$$

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

$$x=\log_{3}\left(27\right)$$

Solve for x (complex solution)

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

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