Solve 5*3^2x=20

$$5 \cdot 3 ^ { 2 x } = 20$$

Solve for x

$$x=\log_{3}\left(2\right)\approx 0.630929754$$

Steps Using Definition of Logarithm

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

$$5\times 3^{2x}=20$$

Divide both sides by 5.

$$3^{2x}=4$$

Take the logarithm of both sides of the equation.

$$\log(3^{2x})=\log(4)$$

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

$$2x\log(3)=\log(4)$$

Divide both sides by \log(3).

$$2x=\frac{\log(4)}{\log(3)}$$

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

$$2x=\log_{3}\left(4\right)$$

Divide both sides by 2.

$$x=\frac{2\log_{3}\left(2\right)}{2}$$

Solve for x (complex solution)

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

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