Solve 59=8^3x

$$59 = 8 ^ { 3 x }$$

Solve for x

$$x=\frac{\log_{2}\left(59\right)}{9}\approx 0.653627005$$

Steps Using Definition of Logarithm

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

$$8^{3x}=59$$

Take the logarithm of both sides of the equation.

$$\log(8^{3x})=\log(59)$$

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

$$3x\log(8)=\log(59)$$

Divide both sides by \log(8).

$$3x=\frac{\log(59)}{\log(8)}$$

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

$$3x=\log_{8}\left(59\right)$$

Divide both sides by 3.

$$x=\frac{\log_{2}\left(59\right)}{3\times 3}$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{9\ln(2)}+\frac{\log_{2}\left(59\right)}{9}$$

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