SOLUTION: Solve for xto the nearest hundredth: log7 75=x

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Question 404464: Solve for xto the nearest hundredth: log7 75=x
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%287%2C+%2875%29%29=x
You mean you don't know what power of 7 is 75? Well, neither do I. So just use the base 7 log button on your calculator!

Just kidding. No one's calculator has a base 7 logarithm button. But it probably does have a base 10 (aka log) button and/or a base e (aka ln) button. So if we can express your base 7 log in terms of base 10 or e logs, we can use our calculator. Fortunately we have the base conversion formula: log%28a%2C+%28p%29%29+=+log%28b%2C+%28p%29%29%2Flog%28b%2C+%28a%29%29.

Using the conversion formula we can change to base 10:
log%287%2C+%2875%29%29+=+log%28%2875%29%29%2Flog%28%287%29%29
or to base e:
log%287%2C+%2875%29%29+=+ln%2875%29%2Fln%287%29
Now we can get out our calculators, find the two logarithms and divide them. And believe it or not, it doesn't matter whether we use base 10 or base e logarithms. They both result in the same answer! (Try then both if you don't believe me.)