Question

Log x base p= a, log x base q= b, then prove that log x base p/q = ab/a-b. ​

Answer 1

Answered 5 years ago

If logpx=a and logqx=b then what is the value of logpqx ?

ab/(b-a)

log x (base p) = a

=> x = p^a

log x (base q) = b

=> x = q^b

=> p^a = q^b

=> q = p^(a/b)

=> p/q = p^(1 -a/b)

log x (base p/q)

= log x (base p^(1 - a/b))

= log p^a (base p^(1 - a/b)

= a/(1-a/b)

= ab/(b-a)