SOLUTION: Use law of logarithms to evaluate: log5 ((120·125)/24)= ? *log ((120·125)/24) to the base of 5.

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Question 374256: Use law of logarithms to evaluate:
log5 ((120·125)/24)= ?
*log ((120·125)/24) to the base of 5.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
log%285%2C+%28%28120%2A125%29%2F24%29%29
First, let's reduce the fraction:
log%285%2C+%28%2824%2A5%2A125%29%2F24%29%29
log%285%2C+%28%28cross%2824%29%2A5%2A125%29%2Fcross%2824%29%29%29
log%285%2C+%285%2A125%29%29%29
Since 125+=+5%5E3 this becomes:
log%285%2C+%285%2A5%5E3%29%29%29
log%285%2C+%285%5E4%29%29%29
If you understand logarithms we already know that this works out to be 4. If not, then we can use a property of logarithms, log%28a%2C+%28p%5Eq%29%29+=+q%2Alog%28a%2C+%28p%29%29, to move the exponent out in front:
4%2Alog%285%2C+%285%29%29%29
By definition, log%285%2C+%285%29%29+=+1. So this becomes:
4*1
or
4