The logarithm function

Common bases of logarithms

• Base 10: historically, logarithms were written down in ‘logarithm books’. These books showed all of their logarithms to base 10.
• Base e: natural logarithms. Euler’s number is the ‘natural base’ of logarithms.

Natural logarithm function

Essentially, is just another way of writing . We use all the time in logarithms, so it is easier to write instead of .

Logarithm function constraints

• In the function :

Example: solve for :

• Divide both sides by 3:
• Rewrite the logarithm as a power of :
• Subtract 2 from both sides:
• Therefore, the solution is: