Solve 6^3x=36

$$6 ^ { 3 x } = 36$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps Using Definition of Logarithm

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

$$6^{3x}=36$$

Take the logarithm of both sides of the equation.

$$\log(6^{3x})=\log(36)$$

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

$$3x\log(6)=\log(36)$$

Divide both sides by \log(6).

$$3x=\frac{\log(36)}{\log(6)}$$

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

$$3x=\log_{6}\left(36\right)$$

Divide both sides by 3.

$$x=\frac{2}{3}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(6)}+\frac{2}{3}$$

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