Question

if logx3 = a and logx25 = b, determine an expression for logx(9/5).

Answer 1

logx 3 = a

x^a = 3
x^(2a) = 9 ---> logx 9 = 2a

logx 25 = b
x^b = 25 = 5^2
x^(b/2) = 5 ---> logx 5 = b/2

then logx(9/5)
= logx 9 - logx 5
= 2a - b/2
= (4a-b)/2