Solve 53/5=2^3x

$$53 / 5 = 2 ^ { 3 x }$$

Solve for x

$$x = \frac{\log_{2} {(\frac{53}{5})}}{3} \approx 1.135330787$$

Steps Using Definition of Logarithm

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

$$2^{3x}=\frac{53}{5}$$

Take the logarithm of both sides of the equation.

$$\log(2^{3x})=\log(\frac{53}{5})$$

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

$$3x\log(2)=\log(\frac{53}{5})$$

Divide both sides by \log(2).

$$3x=\frac{\log(\frac{53}{5})}{\log(2)}$$

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

$$3x=\log_{2}\left(\frac{53}{5}\right)$$

Divide both sides by 3.

$$x=\frac{\ln(\frac{53}{5})}{3\ln(2)}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}-\frac{\log_{2}\left(\frac{5}{53}\right)}{3}$$

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