Solve 6^x=50

$$6 ^ { x } = 50$$

Solve for x

$$x=\log_{6}\left(50\right)\approx 2.183341611$$

Steps Using Definition of Logarithm

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

$$6^{x}=50$$

Take the logarithm of both sides of the equation.

$$\log(6^{x})=\log(50)$$

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

$$x\log(6)=\log(50)$$

Divide both sides by \log(6).

$$x=\frac{\log(50)}{\log(6)}$$

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

$$x=\log_{6}\left(50\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(6)}+\log_{6}\left(50\right)$$

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