SOLUTION: Given Log 2=.3010 and log 3 =.4771, find: a. log (240) b. log (1.5)

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.
RELATED QUESTIONS
11) Given log a = 0.3010 and log b = 0.4771, evaluate log 24... (answered by josgarithmetic,greenestamps)

Given log 2=.3010 and log 3=.4771, evaluate log 6 Can you multiply the logs to get the... (answered by MathTherapy)

If log2=.3010 and log 3=.4771 then find... (answered by greenestamps)

given that log2 = 0.3010, log3= 0.4771 and log7= 0.8451 evaluate 1.log(14/3) 2.log (answered by Alan3354)

given log2=.3010, log7= .845, and log3=.4771 find the values of: 1)log28 2)log... (answered by josmiceli)

given log 7=0.8451 and log 2 =0.3010, find the value of log 28. (answered by Alan3354,Theo,ikleyn,MathTherapy)

given log b 2= 0.3562, log b 3=0.5646, log b 5=0.8271 and log b 11=1.2323 evaluate:... (answered by vleith)

Given log 2 = 0.3010, log 3 = 0.4771. Find the value of a) log 12 b) log... (answered by jsmallt9)

Log 2 = 0.301 log 3 = 0.477 log 5 = 0.699 using this information Find:- a) Log 6/5 b)... (answered by Alan3354)