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
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log4 [(6^4)/5] = 4.00896...
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I can't imagine how you would get
that answer without a calculator.
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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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