find in terms of a,b, and c.

Question

Given log2=a, log17=b, log59=c. find log(base 2006) of 425 in terms of a,b,c.

Answer 1

using the change of base formula, you would get

 

log 425 / log 2006....... now 2006 = 2 *17*59 so log2006 = log(2*17*59) = log2 + log17 + log 59 = a+b+c

 

Now log 425 = log(17*25) = log 17 + log 5² = log 17 + 2log 5 = b+2log5

 

So your answer is (b + 2log 5)/(a+b+c).

 

Hope this helped