SOLUTION: what is the decimal approximation of log7 988

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Question 596154: what is the decimal approximation of log7 988
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
To find a decimal approximation for a logarithm it must be a logarithm of a base your calculator "knows": base 10 (common) or base r (natural, ln).

So to find a base 7 logarithm you must use the change of base formula to convert it from a base 7 log into base 10 or base e logs. The change of base formula is:
log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29
(Note that the formula converts a log of one base into two logs of another base.)

I'm going to convert the base 7 log into base e logs:
log%287%2C+%28988%29%29+=+ln%28988%29%2Fln%287%29

Now just get out your calculator (or computer calculator program) and find the two logs and then divide them. (Important: Do NOT divide 988 and 7 and then find the log. It doesn't work right that way.)

And finally, if we had converted the base 7 log to base 10 logs instead, we would still get the same answer!