combine ln(a+b)+5ln(a-b)-4lnc?

Question

Thank you show work

Answer 1

= ln {(a+b)(a-b)^5/ c^4}

There's really no work to show as it is simply applying the properties of logrithms:
log a + log b = log (a+b)
log a - log b = log (a/b)
c log a = log a^c

There's just the 3, so learn them and these problems become pretty easy.

Answer 2

here's the solution, I will let you have the fun of the final answer. Back when logs were taught and calculators were in air conditioned rooms, we used added logs to multiply and subtracted logs to divide. multiplying logs, e.g. 4lnc is the same as ln c^4. so you can combine to one ln. not to be too cryptic, lnX + lnY = ln(X+Y), and lnX- lnY = ln(X/Y).

Answer 3

adding in the log domain is like multiplication in numbers
subtracting in the log domain is like division in numbers
multiplying a log is like raising a number to the power.
so

Here is what i see:

ln (((a+b)(a-b)^5) / c^4)

which can probably be simplied further by doing the multiplication.

Let the others verify my answer

peace

Answer 4

you would distribute ln to a and b AND 5ln to a and b
so it would become
lna+lnb+5lna-5lnb-4lnc
then you can only add together lna and 5lna because they are the only ones with the same variables
so it would become
6lna+lnb-4lnc
and that's your answer!

Answer 5

ln(a + b) + ln (a - b)^5 + ln c ^(- 4)
ln [ (a + b) (a - b)^5 / c^4 ]

Answer 6

1.ln(a+b)+ln(a-b)^5 - ln(c)^4
using property lnr^m=mlnr and vise versa
2.ln(a+b)(a-b)^5 - ln c^4
using property ln[(a)(b)] = ln(a) + ln(b) and vice versa
3. ln { [ (a+b)(a-b)^5 ]/c^4 }
using property ln[(a)/(b)] = ln(a)-ln(b) and vice versa

that's it!................. ln { [ (a+b)(a-b)^5 ]/c^4 }