Question

Expand this log! I give medals!

Answer 1

Ok, actually natural log :)

Answer 2

@ganeshie8

Answer 3

I know division - subtraction.

Answer 4

so the first thing you'll wanna do is apply the 'quotient rule'

Answer 5

ln 2x^6-(x+3)^10 ?

Answer 6

I ment -ln (x+3)^10.

Answer 7

like this?
ln 2x^6 - ln (x+3)^10

Answer 8

I think so.

Answer 9

yaya, you did that rule right.
so lets take care of the powers of 6 and 10 by applying the 'power reduction rule'

Answer 10

bring it in front of ln?

Answer 11

ya,
post up what you get

Answer 12

2 ln 6 - 10 ln (x+3)

Answer 13

ln 2x^6 - ln (x+3)^10
dont forget the x with the 2, and the 6 goes infront
6 ln 2x - 10 ln (x+3)

Answer 14

Thanks, I knew that, just goofed.

Answer 15

yep!
we can expand it a bit more still,
do you see that we can factor out a 2 from the 6 and the 10 coefficeitns?

Answer 16

Yes

Answer 17

ln 2x^6 - ln (x+3)^10
6 ln 2x - 10 ln (x+3)
2 (3 ln 2x - 5 ln(x+3))

Answer 18

Is that it?

Answer 19

ya, i believe so, lemme double check...

Answer 20

Sure

Answer 21

ya, thats it ^_^

Answer 22

Thanks and God bless!

Answer 23

actually, we can use the product rule..

Answer 24

sorry, i just realized that

Answer 25

so the ln 2x can have the product rule applied to it

sorry i over looked that!

Answer 26

Can you show me what you mean?
It's fine!

Answer 27

2 (3 ln 2x - 5 ln(x+3))

looking only at
ln(2x) is the same as
ln((2)x) so 2 times x, now apply the product rule:
ln(2) + ln(x)

re insert this back in:
2 ( 3(ln 2 + ln x) - 5 ln(x+3) )

Answer 28

k, now we are done ^_^ haha

Answer 29

I'm sure your right, but it won't take it. Maybe my input error?

Answer 30

does it need to be "ln(2) + ln(x)" ?

Answer 31

and does it need to be "(5)ln(x+3)" ?

Answer 32

Like this?

Answer 33

u have this right now:
3(3ln(2) + ln(x)) - (5)ln(x+3)
do it like this:
3(3(ln(2) + ln(x)) - (5)ln(x+3))
do you see what u were missing? a "(" and a ")"

Answer 34

Still says wrong :(

Answer 35

I can ask my my teacher. Thanks !

Answer 36

hmm....

Answer 37

oh, haha, i found it:
we kept putting in
3(3(ln(2) + ln(x)) - (5)ln(x+3))

but it should be:
2( 3( ln(2) + ln(x) ) - (5)ln(x+3) )

some how we got a 3 out infront, but it should be a 2.