Help with Logarithm questions.?

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.