4 Change of base
Suppose you have logax and you want to find logbx.
Taking logarithms to base a gives:
Rearranging this, gives:
Thus, if you want to change between natural logarithms and logarithms to the base 10, you can use the following:
Try putting this idea into practice now.
Activity 5 Finding logs
Find log9(x) given that log3x = 12
Hint: Can you express any of the numbers in the form 3n.
Remember that logaa = 1, so log33 = 1
You may well have not come across logarithms in this way before, so don’t worry if you needed to take your time to work your way through this week. Practice is so often the key to success with maths, so the next section is your chance to check your understanding and application of these ideas.