Question

Is there a formula for y*ln(x)?

Answer 1

I was doing an integral with partial fractions and now I have to simplify this:
\[2\ln(7)+3\ln(6)-2\ln(6)-3\ln(5)\]

Answer 2

The correct answer is \[2ln(7/3)+\ln(2)\] but how did they get that?

Answer 3

or maybe I did the integral wrong

Answer 4

\[\int\limits_{3}^{4}\frac{ 5x+5 }{ x^2+x-6 }dx\]

Answer 5

\[\frac{ A }{ x+3 }+\frac{ B }{ x-2 }=\frac{ 5x+5 }{ (x+3)(x-2) }\]

Answer 6

your answer has not variables in it!!

Answer 7

I got that
\[A = 2\]
and \[B = 3\]

Answer 8

i know we are evaluating an integral

Answer 9

ooh i see a definite integral

Answer 10

I was thinking that a formula like that would be useful in simplifying it

Answer 11

yah i know its definite

Answer 12

just let me know if i am doing the integral wrong

Answer 13

partial fractions are right

Answer 14

So now it becomes
\[\int\limits_{3}^{4}\frac{ 2 }{ x+3 }+\frac{ 3 }{ x-2 }dx\]

Answer 15

Yah i think i an doing the evaluating step wrong

Answer 16

\[2\log(x+3)+3\log(x-2)\]

Answer 17

yah i did that

Answer 18

i am having trouble simplifying the logs

Answer 19

\[2\log(7)+3\log(2)-2\log(6)\]

Answer 20

there are a lot of ways to write this

Answer 21

so it wouldn't it be\[2\log(7)+3\log(2)-2\log(6)-3\log(1)\]

Answer 22

because you also have to subtract 3log(3-2)

Answer 23

for example
\[\log(\left(\frac{7^2\times 2^3}{6^2}\right)\]

Answer 24

or 3log(1)

Answer 25

i kinda ignored the log of one, since the log of one is zero

Answer 26

oh ok

Answer 27

so now should i use the subtraction property of logs?

Answer 28

what form are you trying to get it in? you want to write it as a single log, use the one i wrote above
there are lots and lots of ways to write it

Answer 29

it would be\[2\log(\frac{ 7 }{ 6 })+3\log(2)\]

Answer 30

no i know that the answer should be log(7/3)+log(2)

Answer 31

but i don't know how they got that

Answer 32

i wouldn't worry about it
why write one part as a single log, then leave the other as a piece by itself? that doesn't make any sense

Answer 33

so is my answer correct?

Answer 34

i got
\[\log\left(\frac{7^2\times 2^3}{6^2}\right)\] writing as a single log, but i didn't do any further arithmetic
lets see if we can make it look like what you want

Answer 35

ok i see

Answer 36

\[\frac{7^2\times 2^3}{6^2}=\frac{7^2\times 2}{3^2}=\left(\frac{7}{3}\right)^2\times 2\]

Answer 37

ok now i see how they got it

Answer 38

argh typo there

Answer 39

thank you

Answer 40

oh no that is right
yw