Let log 2 = a, log 3 = b and log 7 = c. Express the indicated logarithm in terms of a, b, and c.

Question

1-log3 5 (3 is the subscript of the log)

ans:(1-a)/b, i need someone to show me the step bcus my ans is different from the given ans. my ans=(1/a)-b.

Answer 1

remember that log₃ 5 = log 5/log 3

so 1 - log₃ 5
= 1 - log5/log3
now we know 5 = 10/2
so log 5 = log(10/2) = log10 - log2
= 1 - log2
= 1 - a

so
1 - log5/log3
= 1 - (1-a)/b

= (b -1+a)b

My answer is correct, I checked and worked it out on a calculator.