SOLUTION: Given log 2 = 0.3010, log 3 = 0.4771. Find the value of a) log 12 b) log 5.

Question 387532: Given log 2 = 0.3010, log 3 = 0.4771. Find the value of a) log 12 b) log 5.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
These problems are meant to test your understanding of the three main properties of logarithms:

These properties allow us to rewrite logarithms of products, quotients or powers in terms of other logarithms.

In your case we are trying to find the log(12) and the log(5) using the logarithms you were given and a logarithm you should know. So we want to expression 12 and 5 as a product, quotient or power of number(s) whose logarithm you were given or whose logarithm you should know.

log(12)
One way to find this logarithm is as follows:
log(12) = log(2*2*3)
This expresses 12 as a product of numbers whose logarithms you were given. We can use the first property above to split this logarithm into the sum of the logarithms of the factors:
log(12) = log(2*2*3) = log(2) + log(2) + log(3)
Now we just have to replace these three logarithms with the decimals you were given for them and them add them together. (I'll leave the rest for you to finish.

log(5)
5 is not a product of any combination of 2's and/or 3's. Nor is it quotient or power of any combination of 2's or 3's. But it is the quotient of 10 and 2. You were given log(2) and you should know what log(10) is (since the base of log is 10). So
log(5) = log(10/2)
Using the second property, for quotients, we can rewrite this logarithm as the difference of the logarithms of the numerator and denominator:
log(5) = log(10/2) = log(10) - log(2)
You were given log(2), log(10) = 1. (I'll leave it up to you to replace the two logarithms and subtract.)
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