Solve 3714=2^(x/3)

$$3714 = 2 ^ { ( x / 3 ) }$$

Solve for x

$$x=3\left(\log_{2}\left(1857\right)+1\right)\approx 35.5762743$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$2^{\frac{x}{3}}=3714$$

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

$$2^{\frac{1}{3}x}=3714$$

Take the logarithm of both sides of the equation.

$$\log(2^{\frac{1}{3}x})=\log(3714)$$

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

$$\frac{1}{3}x\log(2)=\log(3714)$$

Divide both sides by \log(2).

$$\frac{1}{3}x=\frac{\log(3714)}{\log(2)}$$

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

$$\frac{1}{3}x=\log_{2}\left(3714\right)$$

Multiply both sides by 3.

$$x=\frac{\log_{2}\left(3714\right)}{\frac{1}{3}}$$