Solve 6^x/2=34

$$\frac { 6 ^ { x } } { 2 } = 34$$

Solve for x

$$x=\log_{6}\left(68\right)\approx 2.354952089$$

Steps Using Definition of Logarithm

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

$$\frac{1}{2}\times 6^{x}=34$$

Multiply both sides by 2.

$$6^{x}=68$$

Take the logarithm of both sides of the equation.

$$\log(6^{x})=\log(68)$$

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

$$x\log(6)=\log(68)$$

Divide both sides by \log(6).

$$x=\frac{\log(68)}{\log(6)}$$

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

$$x=\log_{6}\left(68\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(6)}+\log_{6}\left(68\right)$$

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