SOLUTION: Given Log<c> 2=0.387, log<c>3=0.613, and log<c>5=0.898, find log<c> 16875/2 The "<c>" is meant to be a subscript. The answers are [A] 4.044 [B] 7.044 [C] 50.440 [D] 5.044

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given Log<c> 2=0.387, log<c>3=0.613, and log<c>5=0.898, find log<c> 16875/2 The "<c>" is meant to be a subscript. The answers are [A] 4.044 [B] 7.044 [C] 50.440 [D] 5.044       Log On


   

Question 866646: Given Log 2=0.387, log3=0.613, and log5=0.898, find log 16875/2 The "" is meant to be a subscript. The answers are [A] 4.044 [B] 7.044
[C] 50.440 [D] 5.044 Honestly I have no idea how to do this problem, today in Math we learned how to manipulate logarithms, so I am familiar with adding and subtracting logarithms in order to make it a complex or seperate logarithm(s). Thank you so much for your help
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try completely factoring the 16875 into its prime factorization.
16875=9%2A1875=9%2A25%2A75=highlight_green%283%5E2%2A5%5E2%2A2%2A5%5E2%29.

log%28%2816875%2F2%29%29=log%28%2816875%29%29-log%28%282%29%29
log%28%282%2A3%5E2%2A5%5E4%29%29-log%28%282%29%29
You should be able to continue from here and finish.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Given Log 2=0.387, log3=0.613, and log5=0.898, find log 16875/2 The "" is meant to be a subscript.
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log(16875/2) = log(16875)-log(2)
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Note: 16875/5 = 3375
3375/5 = 675
675/5 = 135
135/5 = 27
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27 = 3^3
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So,: log16875) = log(5^4*3^3) = 4log(5)+3log(3) = 4*0.898+3*0.613 = 5.431
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Ans: log[16875/2] = 5.431-0.387 = 5.044
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Cheers,
Stan H.
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The answers are [A] 4.044 [B] 7.044
[C] 50.440 [D] 5.044