SOLUTION: how do u simplify log7 7^5

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Question 283777: how do u simplify log7 7^5
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%287%2C+%287%5E5%29%29
If you understand what logarithms are, you can see what the answer is. In general, log%28a%2C+%28b%29%29 represents the exponent for "a" that results in "b". Your specific logarithm represents the exponent for 7 that results in 7%5E5. And what exponent do you put on 7 to get 7%5E5? Answer: 5, of course!.

Another way to figure this out is to use the property of logarithms,
Since log%287%2C+%287%29%29+=+1 by definition, this simplifies to 5.

A last resort way to do this is to use the base conversion formula, log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29, to convert your logarithm into one your calculator "knows". Using this formula to convert your base 7 logarithm into an expression of base 10 logarithms we get
log%28%287%5E5%29%29%2Flog%28%287%29%29
Now you can use your calculator on this. The reasons this is a last resort method are:
  • Calculators use rounded-off decimal approximations for most logarithms. So your calculator may end up telling you the answer is something like 5.00000001 or 4.99999999 instead of the 5 it should be.
  • This is longer and more difficult, even with a calculator, than the other methods.