Logarithum expansion

Question

completely expand the logarithmic expression:

 

log₆(36ab²/c√d)

 

I have a decent understanding of how to expand the denominator but the numerator is unclear to me.

Thank you for the help, it is much appreciated.

Answer 1

Because you have a numerator and denominator, your log terms will have positive and negative signs when expanded.

 

Any log term in the numerator has a positive sign.  Any log term in the denominator has a negative sign.

 

 

For example,

 

log((2b) / (4gh)) =

 

log(2) + log(b) - log(4) - log(g) - log(h)