A logarithm is when you take a number to a specific power so that the result is another number. For example, if you multiply 2 by itself 5 times, we can say that “2 to the power of 5” equals 32. We also say that “2 to the power of 5” equals 32. You can also write these as log₅(32) = 2.

## What is a logarithm?

If you’ve ever had to solve an exponential equation, you know that it can be a time-consuming process. Luckily, logarithms help make these equations much easier to work with. Let’s define what a logarithm is and how it works.

A logarithm is a mathematical function that represents the power to which one number needs to be raised in order for another number (its base) to equal the result. This definition may sound complicated, but don’t worry—you’ll soon get used to it!

## Exponentiation

In mathematics, exponentiation is the repeated multiplication of a number by itself. The base is the number that is being raised in power, while the exponent is a single digit or an expression that shows how many times this operation has been performed on a given base. In other words, x^2 means “x squared,” x^3 means “x cubed” and so on.

## Logarithm multiplication rules

To multiply two logarithms, you can rewrite them so they have equal bases first; then you can use regular multiplication rules to combine like terms. For example, if you want to know what 2^a + 5^b equals in terms of a and b variables: First write out each expression with different bases (2 and 5). Then rewrite so that both expressions have a base of 10; this makes sure all variables are present in both equations for easy comparison later on! You end up with 2a = 50b; now use regular multiplication rules to solve for all unknowns: `2a = 100b which means 2a = 50b/2 or 25b = 100b/4 or b=25

## Logarithm exponent rule

Logarithms can be used to find the logarithms of a product, quotient, or power. The general rule for finding the logarithm of a product is that the logarithm of a product is equal to the sum of the logarithms of each factor. In other words, if you have a^x and b^y and you want to find their product’s logarithm, then:

\log {a \times b} = y + x

For example: If you have 2^3 and 3^2 as your expressions then their logs would be 6 and 9 respectively because 2 * 3 = 6 (6 * 2 = 12) and 3 * 3 = 9 (9 * 3 = 27).

Logs also work with ratios between numbers rather than factors. For example: If you have 4/5 as an expression then its log would be -1 because 4 / 5 is equivalent to -1 / 1 in terms of logs where -1 represents 0 decimals since it’s negative but still positive overall since we’re working with fractions here!

## Example: using the expanding logarithms calculator

The expanding logarithms calculator has three different modes depending on what you need. Using it is as easy as entering your current values and reading out the result.

For more logarithm-related calculators you can check out the Negative Log Calculator, the Condense Logarithms Calculator, and the Antilog Calculator!

## FAQ

What are logarithms?

A logarithm is a mathematical function that represents the power to which one number needs to be raised in order for another number (its base) to equal the result.

What is a natural logarithm?

A natural logarithm has e (Euler’s number) as its base.

What is exponentiation?

Exponentiation is the repeated multiplication of a number by itself.