Solve 1=64^2x

$$1 = 64 ^ { 2 x }$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

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

$$64^{2x}=1$$

Take the logarithm of both sides of the equation.

$$\log(64^{2x})=\log(1)$$

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

$$2x\log(64)=\log(1)$$

Divide both sides by \log(64).

$$2x=\frac{\log(1)}{\log(64)}$$

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

$$2x=\log_{64}\left(1\right)$$

Divide both sides by 2.

$$x=\frac{0}{2}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{6\ln(2)}$$

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