Submitted by Speedscarlet on Thu, 11/24/2016 - 09:27
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If log36=a and log 125=b, express log(1/12) in terms of a and b.
Submitted by Speedscarlet on Thu, 11/24/2016 - 09:27
If log36=a and log 125=b, express log(1/12) in terms of a and b.
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Are you asking for help with this or suggesting it as a nice problem for others to think about?
Asking for help
Asking for help
Special Numbers
If I've got this right...
Hint 1
36 and 125, are special numbers (but in slightly different ways). Do you recognise them?
Hint 2
I had to make the question more user friendly by connecting the logs I knew with what I had been asked about. After that there was algebra to be done, but it was only a few lines.
Hope that is a) correct(!) and b) not too mysterious.
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logarithms
Try using the fact that 36 is a square number and 125 is a cube number. Then try using some of the log rules to rearrange it into a form more similar to that of the answer.
More Hints
After breaking down 36 and 125 you will have two simplified log expressions. Don't simplify log 36 completely, it's not helpful, just use the square fact.
It is also helpful to write $\frac 1 {12}$ as another equivalent fraction. It is also helpful to note that
log (10)=1.