Scientists Say: Logarithm

This math function is just another way of working with exponents

Logarithms provide a way to figure out how many times a number must be multiplied by itself to get another number.

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Logarithm (noun, “LOG-uh-rih-thəm”)

A logarithm refers to the number of times you must multiply a number by itself to get another number.

You can think of logarithms as another way of working with exponents. In math, an exponent is a number that appears as a superscript after another number:

52 = x

In this equation, 2 is the exponent. The number 5 is called the base. The base is the number that will be multiplied by itself. Here’s how we solve this equation:

52 = 5 × 5 = x

If we solve for x, that gives us 25. If the exponent changes to 3, we must multiply 5 by itself one more time:

53 = 5 × 5 × 5 = x

In this case, solving for x gives us 125.

How does this relate to logarithms? Logarithms offer another way to solve these same types of equations. The difference is that we solve for a different x. The exponent equation above asks, if I multiply 5 by itself this many times, what number will I get? For 52, the answer is 25.

On the other hand, a logarithm starts out knowing that number is 25, and it asks: How many 5s must I multiply together to get 25? The answer is 2.

This is how mathematicians represent this idea:

Log5(25) = x

And this is how mathematicians represent the answer:

Log5(25) = 2

Spoken out loud, we would say: The logarithm (Log) of 25 to base 5 equals 2.

This equation asks, to what power — or exponent— must you raise 5 in order to get 25? That means logarithms are just a way to solve for an unknown exponent.

Logarithms help scientists just like exponents do. Scientists sometimes use logarithms to display their data. A logarithmic scale comes in handy when scientists want to show exponential changes over time. For example, scientists may use a logarithmic scale to display bacterial growth in a petri dish. The pH scale for acidity also operates on a logarithm base 10 scale.

In a sentence

Logarithms allowed scientists to develop a math equation that converts dog years into people years.

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Katie Grace Carpenter is a science writer and curriculum developer, with degrees in biology and biogeochemistry. She also writes science fiction and creates science videos. Katie lives in the U.S. but also spends time in Sweden with her husband, who’s a chef.