Solve 6^3x-4div6^2=216

$$6 ^ { 3 x - 4 } \div 6 ^ { 2 } = 216$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$\frac{1}{36}\times 6^{3x-4}=216$$

Multiply both sides by 36.

$$6^{3x-4}=7776$$

Take the logarithm of both sides of the equation.

$$\log(6^{3x-4})=\log(7776)$$

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

$$\left(3x-4\right)\log(6)=\log(7776)$$

Divide both sides by \log(6).

$$3x-4=\frac{\log(7776)}{\log(6)}$$

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

$$3x-4=\log_{6}\left(7776\right)$$

Add 4 to both sides of the equation.

$$3x=5-\left(-4\right)$$

Divide both sides by 3.

$$x=\frac{9}{3}$$

Solve for x (complex solution)

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

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