Find the logarithms of the following numbers to the base 2:
(...)
What is the format of the answer?
This is usually written as:
$$\log_{2} 32$$
I know 32 is 2^5.
This is indeed equal to $5$ for exactly that reason:
$$\log_{2} 32 = 5 \iff 2^5 = 32$$
Or in general (for $a>0$ and $a \ne 1$, $x>0$):
$$\log_{a} x = y \iff a^y = x$$
This is usually written as: $$\log_{2} 32$$
This is indeed equal to $5$ for exactly that reason: $$\log_{2} 32 = 5 \iff 2^5 = 32$$ Or in general (for $a>0$ and $a \ne 1$, $x>0$): $$\log_{a} x = y \iff a^y = x$$