Can you explain what a logarithm is?

We can think of taking the logarithm base a of a number b (log_ab) as "the number of times we need to multiply a by itself to get b". So for example, log₂ 16 = 4, since we need to multiply 2 by itself 4 times to get 16 (2 x 2 x 2 x 2 = 16, or 2⁴ = 16).In more detail, logarithms are the inverse operations to exponentiation. This means that if you are given a number x and told to raise y to the power of x to get z, then log_y z = x. i.e. if we have the operation "raise y to the power of ___", then performing the operation "take the logarithm base y" gives us back our original input ____. So if y^x = z, then performing the inverse operation to both sides gives us back x: log_y y^x = log_y z ==> x = log_y z