ELI5: logarithms change of base
// explanation
What is the change of base formula?
The change of base formula lets you switch a logarithm from one base to a different base, kind of like converting inches to centimeters [5]. Imagine you have a question asking "what power do I raise 2 to get 8?" but your calculator only works with base 10 — the change of base formula helps you answer it anyway [2].
Why do we need to change bases?
Sometimes the base you're working with isn't convenient for your calculator or the problem you're solving [2]. Most calculators have buttons for "log" (base 10) and "ln" (base e), so if you need a different base, you need a way to convert it [2].
How does it actually work?
The formula says that if you want to find log base b of x, you can divide log base a of x by log base a of b, where a is any base you choose [2]. It's like saying "the number of steps to go from b to x equals the number of steps from b to a times the number of steps from a to x" [3].
When would you use it?
You'd use the change of base formula when your calculator doesn't have the base you need, or when you're simplifying expressions with different bases [1].
// sources
Jan 30, 2018 ... This algebra video tutorial explains how to use the change of base formula to evaluate logarithms. Logarithms - Free Formula Sheet: ...
You can change the base of your logarithm to any base using the change of base rule. "ln" (log base e) and "log" (log base 10) are the most common bases used ...
Dec 28, 2017 ... The change of base rule then tells us that the exponent from b to x is equal to the exponent from b to a times the exponent from a to x.
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number.
The change of base formula is a formula for expressing a logarithm in one base in terms of logarithms in other bases.
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