Hi everyone, Before calculators were invented, people used logarithms.

Numbers with exponents are usually written like this: x=b^y

In logarithms, this is written as y = log_bx

So basically, logarithms helps show the exponent.

an example: 

logarithm form:  

In a way it's like asking, how many 2s are there in 8?

This is actually defined as the inverse function of indicial function y = a^x.

It's domain ( range  of possible values when y is the independent variable): 0, +infinite

It's range (range of possible values when x is the independent variable - "normal graph"): -infinite, +infinite

 

Logarithmic function: The graph of a^x (blue) as opposed to log_ax (red), when a is bigger than 1. As you can see, for a > 1, the graph is always increasing

For 0

logarithmic identity: 

since like x = a^y--------- (1), and y = log_ax-------- (2), substituting y in (1), we have x = 

Thanks :)

etzhkyay

Sources (logarithm graphs): http://www.regentsprep.org/Regents/math/algtrig/ATP8b/exponentialFunction.htm