Prove that log(a) b = 1/(log(b) a)

1 Answer

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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)`

This proves that `log_a b = 1/(log_b a)`