SOLUTION: 4log4 6 - log 4 5, evaluate without a calcuator
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Question 235481: 4log4 6 - log 4 5, evaluate without a calcuator
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4log4 6 - log 4 5, evaluate without a calculator
-------------------
log4 [(6^4)/5] = 4.00896...
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I can't imagine how you would get
that answer without a calculator.
-------------------
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The best I can do without a calculator is to express this in terms of a single logarithm.
Use
To write:
Then use: The difference of the logs is the log of the quotient, that is:
to write:
I need at least a scratch pad to go any further:
,
,
Now, if you want to do this the old fashioned way with a table of logarithms, you aren't likely to find a table of base 4 logs. That means you will have to do a base conversion.
Here's the formula:
So, for your situation:
Then you would have to look up
and
, then interpolate to find
.
To interpolate:
.
Finally, calculate
.
Next, look up
and divide it into the results of the last step -- by hand, of course.
Good luck.
John

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