SOLUTION: log_8 (1/4) =

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Question 238097: log_8 (1/4) =
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


There are two ways to do this one.

Method 1: Definition of Logarithms

Use the fact that



To write



But since we can say and since we can say

Therefore



hence





Method 2: Base Conversion

Calculators and Log Tables do not support direct look up of logs other than base 10 or base e (natural) logs. But you can do a base conversion:



Where , or (it doesn't matter -- you can use either), and

So, using :




Use your calculator or a natural log table to fill in the values of and , and then do the quotient to calculate the value.

Go here for an on-line natural log table: http://myhandbook.info/table_naperlog.html

John