Question

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

Answer 1

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)