Question

How does ln(5) - ln(4) - ln(6) + ln(5) simplify to ln(25/24).

I understand that ln5-ln4 = ln(5/4), not sure if that helps to simplify, but I don't see it.

Answer 1

do you know your log laws? :)
If you SUBTRACT ln(x) - ln (y) = ln (x/y) because you DIVIDE.
If you ADD ln (x) + ln (y) = ln (xy) because you MULTIPLY.
So theeeenn
ln (5) - ln (4) - ln (6) + ln (5)
= ln ( 5 divided by 4 divided by 6 times 5)
So to break it down:
ln (5) - ln (4) = ln (5/4) right?
Then ln (5/4) - ln (6)
= ln (5/24)
Then ln (5/24) -ln (5)
= ln (5/24 * 5)
= ln (25/24)

Answer 2

ah very nice :), ty @butterflydreamer, and all else

Answer 3

you're welcome! :)
Hope you get it xD Looks kinda confusing