Solve 32^6=2^x

$${ 32 }^{ 6 } = { 2 }^{ x }$$

Solve for x

$$x=30$$

Steps Using Definition of Logarithm

Calculate 32 to the power of 6 and get 1073741824.

$$1073741824=2^{x}$$

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

$$2^{x}=1073741824$$

Take the logarithm of both sides of the equation.

$$\log(2^{x})=\log(1073741824)$$

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

$$x\log(2)=\log(1073741824)$$

Divide both sides by \log(2).

$$x=\frac{\log(1073741824)}{\log(2)}$$

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

$$x=\log_{2}\left(1073741824\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(2)}+30$$

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