Anna D.

asked • 10/31/15

what is log_3 (9/squareroot 3) ?

I don't understand logs so i really need step by step

1 Expert Answer

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Philip P. answered • 10/31/15

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log3(9/√3)
 
     = log3(32/31/2)
 
Now use the log rule log(a/b) = log(a) - log(b)
 
     = log3(32) - log3(31/2)
 
     = 2 - 1/2 = 3/2
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Andrew M.

Note that when you see an elment such as
logbx
 
The actual thing it is asking is
"To what power would I raise the base 'b' to get the value 'x'?
 
Example:  log28 = 3   because   23 = 8
               log416 = 2  because 42 = 16
 
So..  logxxn = n
 
We have log3(9/√3)
 
You can work it out the way Philip P. did or you
can reduce the 9/√3 down since both are powers of 3
 
9/√3 = 32/31/2 = 32-1/2 = 33/2
 
log333/2 = 3/2
 
Look at the last line above.  It asks:
To what power would I raise 3 to get
33/2 ...   The answer is 3/2
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11/01/15

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