SOLUTION: If log2=0.3010 and log3=0.4771, find the value of : 7 log 10/9 -2 log 25/24 +3 log 31/80

Question 279144: If log2=0.3010 and log3=0.4771, find the value of :
7 log 10/9 -2 log 25/24 +3 log 31/80
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

I don't think the problem can be done without a calculator with that 31 in there. So I am going to assume that the 31 should be an 81 instead:

I am going to start by factor the numbers in the arguments into prime factors:

Next I'll use the property of logarithms, , to move the coefficients of the logarithms into the arguments as exponents:

Using rules for exponents in the argument to simplify we get:

Next I'll use the properties of logarithms:

to combine the three logarithms into one:

Now we simplify this:

which, by the information you've been given is 0.3010
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