Question

Prove log base 1/b of a = log base b of 1/a

Answer 1

Answer:

We have to prove that log_a b = 1/(log_b a)

Use the property for changing the base of logarithms: log_a b = (log_c b)/(log_c a)

Change the base of log_a b to b

log_a b = (log_b b)/(log_b a)

Use the property: log_b b = 1

=> 1/(log_b a).