Question 280937: Given Log 2=.3010 and log 3 =.4771, find:
a. log (240)
b. log (1.5)
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! With the two given values for base 10 logarithms and since we know that log(10) = 1 by definition, we can find the log(240) and log(1.5) without a calculator if we are somehow able to express them in terms of log(2), log(3) and/or log(10).
The tools we have for this task are the properties of logarithms:
These properties allow us to rewrite logarithms of products, quotients or powers in terms of other logarithms. So we will be trying to use these properties to rewrite log(240) and log(1.5) as products, quotients and/or powers of 2, 3 and/or 10.
If we factor 240 we find that its factors are all 2's, 3's or 10's!:
log(240) = log(2*2*2*3*10)
Using the first property mentioned above we get:
log(240) = log(2) + log(2) + log(2) + log(3) + log(10)
We can now replace each of these logs with their know values and add them all together.
For log(1.5) we can rewrite 1.5 as a quotient of 3 and 2:
log(1.5) = log(3/2)
And we can use the second property to rewrite this:
log(1.5) = log(3) - log(2)
Now we can use the given values for these logarithms and subtract them.
I'll leave the actual additions and subtractions up to you.
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