SOLUTION: how do u simplify log7 7^5

Question 283777: how do u simplify log7 7^5
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

If you understand what logarithms are, you can see what the answer is. In general, represents the exponent for "a" that results in "b". Your specific logarithm represents the exponent for 7 that results in . And what exponent do you put on 7 to get ? Answer: 5, of course!.

Another way to figure this out is to use the property of logarithms,
Since by definition, this simplifies to 5.

A last resort way to do this is to use the base conversion formula, , 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

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.

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