It is given that a = b*c.
Take the logarithm to any base B of both the sides.
`log_B a = log_B(b*c)`
Use the property `log_B a*b = log_B a + log_B b`
=> `log_B a = log_B b + log_B c`
The given relation is equivalent to `log_B a = log_B b + log_B c`
So that? Let ya explain more please: