What is a Logarithm

Algebra 2 Tutorial

What is a Logarithm


For every function there is an inverse function. If y can be written as an expression of x, then, inversely, x can be written as an expression of y.

For example, say you know that
x = \frac{y}{2}}

An exponential, like all functions, has an inverse. That inverse is called a logarithm. So if…

x^3 = y
3= log_xy

So the expression c=log_ab can be understood to mean that c is the number that a must be raised to in order to equal b.

The subscript in the logarithm is called the base. Logarithms to the base 10 are called common logs.
Logarithms to the base e (an irrational number) are called natural logs

Sample Problem

Assuming the following statement is true, determine the value of x

x= log_5125




Therefore 5^3=125 and so

log_5125 = 3

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