Logarithm concepts

Suppose you are a biologist investigating a population that doubles every year. So if you start with 1 specimen, the population can be expressed as an exponential function: $p(t)=2^t$ where $t$ is the number of years you have been watching, and $p$ is the population.

Question: How long will it take for the population to exceed 1,000 specimens?

We can rephrase this question as: “2 to what power is 1,000?” This kind of question, where you know the base and are looking for the exponent, is called a logarithm .

${\text{log}}_2\text{1000}$ (read, “the logarithm, base two, of a thousand”) means “2, raised to what power, is 1000?”

In other words, the logarithm always asks “ What exponent should we use ?” This unit will be an exploration of logarithms.

A few quick examples to start things off

As you can see, one of the most important parts of finding logarithms is being very familiar with how exponents work!