Question

Prove that a^log_cb = b^log_ca

Answer 1

Let x = a^log_cb, y = b^log_ca 

∴ log x = log [a^log_cb], log y = log [b^log_ca]

∴ log x = log_cb log a, log y = log_ca log b

∴ log x = `log"b"/log"c".log"a", logy = log"a"/log"c".log"b"`

∴ log x = log y

∴ x = y

∴ a^log_cb = b^log_ca