Solve 1/4=2^6x

$$\frac { 1 } { 4 } = 2 ^ { 6 x }$$

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps Using Definition of Logarithm

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

$$2^{6x}=\frac{1}{4}$$

Take the logarithm of both sides of the equation.

$$\log(2^{6x})=\log(\frac{1}{4})$$

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

$$6x\log(2)=\log(\frac{1}{4})$$

Divide both sides by \log(2).

$$6x=\frac{\log(\frac{1}{4})}{\log(2)}$$

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

$$6x=\log_{2}\left(\frac{1}{4}\right)$$

Divide both sides by 6.

$$x=-\frac{2}{6}$$

Solve for x (complex solution)

$$x=\frac{i\pi n_{1}}{3\ln(2)}-\frac{1}{3}$$

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