Sheeba B.

asked • 10/03/15

i cant solve this problem please help me to solve

if log2=0.3010, log3=0.4771, log7=0.8451, then find the value of log75

Jordan K.

I believe the reason why you can't solve this problem is that the prime factors of 75 are 3,5,5.  Numbers 2 and 7 are NOT prime factors of 75.  Therefore, it's impossible to express the number 75 in terms of the product of the given numbers (2,3,7) and so also the log of 75 cannot be expressed as the sum of any combination of the logs for these given numbers. 
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10/03/15

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Arthur D. answered • 10/03/15

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log75=log(52*3)=log(52)+log(3)
log(52)+log(3)
2log(5)+log(3)
2*0.6989+0.4771    log(5)=0.6989
1.3978+0.4771
1.8749
log(75)=1.8749
  
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Jordan K.

Arthur - your solution is correct if she was given the values for log(3) and log(5), but in the problem she was only given the values for log(2), log(3), and log(7) - hence my comment above. 
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10/03/15

Arthur D.

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Jordan-I noticed that too and just assumed that she wrote the wrong logs, maybe the logs for a different problem, or maybe she was given a whole bunch of logs and left log5 out. She was given log3 but not log5 so I just looked up log5 and went from there. Sometimes when I make an assumption I am right and other times I am wrong. Students make a lot of typos and I try to determine what they really meant. Maybe the student will make a comment about the solution.
Thanks for commenting.
Arthur D. 
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10/03/15

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