Solve 94*2^frac{x{3}}=16

$$94 \cdot 2 ^ { \frac { x } { 3 } } = 16$$

Solve for x

$$x=-3\log_{2}\left(47\right)+9\approx -7.663766555$$

Steps Using Definition of Logarithm

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

$$94\times 2^{\frac{1}{3}x}=16$$

Divide both sides by 94.

$$2^{\frac{1}{3}x}=\frac{8}{47}$$

Take the logarithm of both sides of the equation.

$$\log(2^{\frac{1}{3}x})=\log(\frac{8}{47})$$

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

$$\frac{1}{3}x\log(2)=\log(\frac{8}{47})$$

Divide both sides by \log(2).

$$\frac{1}{3}x=\frac{\log(\frac{8}{47})}{\log(2)}$$

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

$$\frac{1}{3}x=\log_{2}\left(\frac{8}{47}\right)$$

Multiply both sides by 3.

$$x=\frac{-\log_{2}\left(47\right)+3}{\frac{1}{3}}$$

Solve for x (complex solution)

$$x=\frac{6\pi n_{1}i}{\ln(2)}-3\log_{2}\left(47\right)+9$$

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