Question 321160: given that log 8=0.9031 and log 9=0.9542 and obviously log 10=1, which logarithm cannot be found without the use of a calculator?
a. log 17 b. log (5/4) c. log 15 d. log 600 e. log 0.4
and also if you could show the work as how you got the answer. thank you so much :)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! given that log 8=0.9031 and log 9=0.9542 and obviously log 10=1, which logarithm cannot be found without the use of a calculator?
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If log8 = 0.9031, then log 2^3 = 0.9031 and 3log2 = 0.9031
Then log(2) = (0.9031/3) = 0.3010
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If log9 = 0.9542, then 2log(3) = 0.9542
Then log(3) = 0.9542/2 = 0.4771
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So now you know the following:
log(2) = 0.3010
log(3) = 0.4771
log(8) = 0.9031
log(9) = 0.9542
log(10) = 1
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a. log 17 cannot be done with the above information
b. log (5/4) = log(10/8) = log(10)-log(8)
c. log 15 = log[3(10/2)] = log(3)+log(10)-log(2)
d. log 600 = log[2*3*2^2*5^2] so can be done
e. log 0.4 = log[(2^2)/10] = 2log(2) - log(10)
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Cheers,
Stan H.
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