Question 1
http://i51.tinypic.com/2ms126s.gif
Question 2
http://i56.tinypic.com/35luvqb.gif
Could you please provide each step and a small explanation? Thanks.
Sorry I had to put in pictures. I didn't know how to write it here so I used an online equation editor.
Tushar
Favorite Answer
Q1:
base change formula is: log(A) to the base B = log(A) to base y/ log(B) to base y (new base "y")
therefore,
log(32) base7 / log(8root2) base 7
= log(32)/log(7) / log(8root2)/log(7) (to the new base, say "a"....it doesn't matter)
=log(32)/log(8root2) ...........(log(7) gets cancelled)
now 32 can be written as 2x2x2x2x2 which is (root2)^10
also 8root2 can be similarly written as 2x2x2xroot2 which is (root2)^7
now by formula log(A^X) = X log(A), we get
log(32)/log(8root2)
= log [(root2)^10)] / log [(root2)^7]
= 10 log(root2) / 7 log(root2)
log (root2) gets cancelled
= 10/7.
Q2:
log (XY) = log(X) + log(Y)
log (X/Y) = log(X) - log(Y)
therefore we get
log [(18x12)/125] / log [42/35]
now rewriting 18x12 as 6^3, 125 as 5^3 and 42/35 as 6/5, we get
log [(6/5)^3] / log[6/5]
= 3 log[6/5] / log[6/5]
= 3.
hope the answers are right. pls check them. but im sure about the methods.
hope this helped you.