explain the steps taken to get to the red arrows

[shadow pike]

i dk how and wat they used to simplify that further please someone explain that to me

<@&791435371564892232>

[fickle forge]

yo

so the first red part

u esseutnailly just group the terms with the same coefficients

so you have

5(ln 5/6 - ln2/3) + 2(ln4/3 - ln5/3)

from here you know that

lna/b = lna - lnb

so u can rewrite the ln5/6 - ln2/3 as

ln 5/4

you can do the same for the ln4/3 - ln5/3 and you get

ln 4/5

now you have

5ln 5/4 + 2ln4/5

from here to here

ln 4/5 = - ln5/4

so you have

5ln5/4 - 2ln5/4

= 3ln5/4

3ln5/4 = ln(5/4)^3 = ln 125/64

[civic sluice]

@shadow pike do you still need help?

[shadow pike]

uhm ig

[civic sluice]

because they followed the log rule

log=ln

[shadow pike]

oh

[civic sluice]

you know the log rules, right ?

[shadow pike]

yh

[civic sluice]

that is what they are doing in this case

[shadow pike]

klm

@civic sluice nd @fickle forge ty for ur help

[civic sluice]

youre welcome