Solve 2^-3x=1/64

$$2 ^ { - 3 x } = \frac { 1 } { 64 }$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$2^{-3x}=\frac{1}{64}$$

Take the logarithm of both sides of the equation.

$$\log(2^{-3x})=\log(\frac{1}{64})$$

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

$$-3x\log(2)=\log(\frac{1}{64})$$

Divide both sides by \log(2).

$$-3x=\frac{\log(\frac{1}{64})}{\log(2)}$$

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

$$-3x=\log_{2}\left(\frac{1}{64}\right)$$

Divide both sides by -3.

$$x=-\frac{6}{-3}$$

Solve for x (complex solution)

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

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