Log Question

Question

Let

 

http://assets.apexlearning.com/Math/200706/19/28725ad1-2ebf-4766-be9e-2eaf434c4696.gif   

 

What is the value of

http://assets.apexlearning.com/Math/200706/20/0d114528-ddb7-45d4-964f-902b7b03c3e0.gif  ?

 

25
4,218.75
33
176

Answer 1

log(A³D⁴/C²)

 

Log identity: log(a/b) = log a - log b.  Hence

 

log(A³D⁴/C²) = log(A³D⁴) - log(C²)

 

Log identity: log(ab) = log(a) + log(b).  hence:

 

log(A³D⁴) - log(C²) = log(A³) + log(D⁴) - log(C²)

 

Log identity: log(a^b) = b*log(a).  Hence:

 

log(A³) + log(D⁴) - log(C²) = 3log(A) + 4log(D) - 2log(C)

 

Now log(A)=3, log(D)=5, log(C)=2:

 

3log(A) + 4log(D) - 2log(C) = 3*3 + 4*5 - 2*2 = 9+20-4 = 25