Solve 6^2x-10=36

$$6 ^ { 2 x - 10 } = 36$$

Solve for x

$$x=6$$

Steps Using Definition of Logarithm

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

$$6^{2x-10}=36$$

Take the logarithm of both sides of the equation.

$$\log(6^{2x-10})=\log(36)$$

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

$$\left(2x-10\right)\log(6)=\log(36)$$

Divide both sides by \log(6).

$$2x-10=\frac{\log(36)}{\log(6)}$$

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

$$2x-10=\log_{6}\left(36\right)$$

Add 10 to both sides of the equation.

$$2x=2-\left(-10\right)$$

Divide both sides by 2.

$$x=\frac{12}{2}$$

Solve for x (complex solution)

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

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