This video introduces solving equations where the letter you are asked to find the value of is in the index (also called the exponent). This requires the use of logarithms. The definition of a logarithm is, if:
logac = b
When we read the line above, we say “log to the base ‘a’ of ‘c’, is equal to 'b'”.
Another way we can think about logarithms is as the inverse of the exponential: for example, if we have a number x, and we put a number, say, 5 to the power of x.
and then we put that to the log of base 5:
that is equal to x:
log5(5x) = x
In other words, if we start with x, and then put 5 to the power of x, we can think of the log process as “undoing” the process of putting 5 to the power of x. So these two processes are the inverse of each other, in a similar way to multiplication and division being the inverse of each other (that is, if you start with x, then multiply by 5, then divide by 5, you get back to x).
Need more of an introduction to the nature of logs? Look at one of the links below before watching this video.
As well as having an understanding of the nature of logs, it is useful to revise your knowledge of the number “e” before watching this video. Remember, “e” is an irrational number that has many real world applications, and that's why it has been given a special name. In fact, “e” is similar to the number π, which is also an irrational number that has a special name because of its applications. The number “e” is approximately equal to 2.718, however, most calculators have a dedicated button for it.
Comfortable with using logarithms and the number “e”? Then you're ready for this video!