SOLUTION: log_8 (1/4) =
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Question 238097: log_8 (1/4) =
Answer by solver91311(24713) (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
 \ \ \Rightarrow\ \ b^y = x)
To write
 \ \ \Rightarrow\ \ 8^y = \frac{1}{4})
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:
\ =\ \frac{{\log _c \left( x \right)}}{{\log _c \left( b \right)}})
Where 
, 
or 
(it doesn't matter -- you can use either), and 
So, using :
\ =\ \frac{{\ln \left( \frac{1}{4} \right) }}{{\ln \left( 8 \right)}})
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
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