Logarithms Video 1
Powers and Indices
Logarithms and Indices are very much related. Strictly speaking, logs don't enter the curriculum until you move on to A level but they are easy enough to cope with. I am putting various videos onto this website which I suggest you use in order. Hopefully, I have covered the steps in small jumps which help you to make sense of this subject area.
Powers and Indices
Watch Logarithms Video 1 and then have a go at this exercise.
Exponential Function
A very brief history on the value of e.
Index and logarithm forms
A copy of a historic document: Logarithms and Other Tables for Schools by F. Castle. A touch of nostalgia for those of us of a certain age. The back few pages act as a reminder of how to use the tables.
Using the Laws of Logarithms to combine expressions together to present a simplified version.
Changing logarithms from one base to another can be done on a calculator where you can just put the base number in as required. However, for those of us possessing older calculators (or indeed, log tables booklets), this method will come in handy.
Writing indices with mixed bases as a single index is simple when you understand that logarithms are the opposite to powers. So in the same way as we can undo addition using subtraction, multiploication using division, we can undo powers using logarithms and vice versa.
Find the value of x by raising both sides to the power of ten and then cancelling down.
Solve a natural logarithm problem by raising to the value of e and then rearranging the equations to find the exact value of the unknown.
Using quadratic equations and substitution to find the two values of x in the solution of this problem.