Scientists Say: Logarithm

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

Scientists Say: Exponent

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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