math
posted by Kris on .
Q1: If K=In a In b +In c t/bc,show that K=(ac/b)e^(t/bc).
Q2:Express log(8)5 in terms of m ,where m=lg 2
Q3:Given that log (4)3 =a and log(4)5 =b ,express log(75)16 in terms of a and/or b .
really don't know how to do these qns..please help ! thanks a lot

Q1
ln a ln b +ln c = ln ac/b
so, e^K = e^(ln ac/b) e^(t/bc) = ac/b e^(t/bc)
Q2
since 8=2^3, log_8(x) = 1/3 log_2(x).
So, log_8(5) = 1/3 log_2(5) = m/3
Q3
log_16(75) = 1/2 log_4(75) = 1/2 log_4(3*5^2) = (a+2b)/2
log_75(16) = 1/log_16(75) = 2/(a+2b)