Solve 2^-364=2^n

$${ 2 }^{ -3 } 64 = { 2 }^{ n }$$

Solve for n

$$n=3$$

Steps Using Definition of Logarithm

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{1}{8}\times 64=2^{n}$$

Multiply \frac{1}{8} and 64 to get 8.

$$8=2^{n}$$

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

$$2^{n}=8$$

Take the logarithm of both sides of the equation.

$$\log(2^{n})=\log(8)$$

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

$$n\log(2)=\log(8)$$

Divide both sides by \log(2).

$$n=\frac{\log(8)}{\log(2)}$$

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

$$n=\log_{2}\left(8\right)$$