Question

Solve the following equation
ln(2x+3)+ln(x-6)=2lnx

Answer 1

simplify using rules of logs
then take e^ both sides to get rid of the lns

Answer 2

Ok thanks

Answer 3

What did you get as your result so far after doing what Peter told you?

Answer 4

@WilliamF You there?

Answer 5

@Azteck Yes, sorry just been a while since I've used log, I'll let you know when I get an answer

Answer 6

Okay, no worries.

Answer 7

Just for your benefit, you need to use the quadratic formula afterwards to find x, since you won't be able to factorise it.

Answer 8

@kyusakazaki Here's some tips for you when helping people on OpenStudy: 1. Please don't give answers away without letting the person know what you're trying to do.
2. Actually guide the person step by step.
3. This is not really a tip, but "ln" is not log to the base 10. It seems you haven't gotten that far ahead in maths to know that "ln" is log to the base "e".

Answer 9

thanks aztek i made a bad mistake

Answer 10

No worries man.

Answer 11

so using rules of logs I get \[\ln \frac{ 2x^{2}-9x+12 }{ x ^{2}}\]
Can't you just cancel out the x^2 then find an answer of x? Although I have a feeling you can't do this

Answer 12

where did you get the denominator from?

Answer 13

Only simplify the LHS. Don't touch anything on the RHS first.

Answer 14

Using log laws:
\[ln(a)+ln(b)=ln(ab)\]
\[ln(2x+3)+ln(x-6)=ln(2x+3)(x-6)\]
Do you follow so far?

Answer 15

@WilliamF You there?

Answer 16

Yes I'm here and follow that part

Answer 17

So that's the LHS done.

Answer 18

Now the RHS.
Using the log law:
\[xlna=lna^{x}\]
The RHS will become:
\[2lnx=lnx^2\]

Answer 19

Do you follow this part as well?

Answer 20

yep, that is where I got the denominator btw

Answer 21

Now we have this:
\[\large ln(2x+3)(x-6)=lnx^2\]
WE can just get rid of the ln.
and we will then have:
\[\large (2x+3)(x-6)=x^2\]

Answer 22

Do you get that? We just e^ both sides.

Answer 23

We don't need to bring the lnx^2 to the LHS.

Answer 24

It's much easier to do that.

Answer 25

If you get that part, then you can continue on expanding the LHS and moving everything to one side. THen you can use the quadratic formula to solve for x. Could you please give me your answer after you've done those steps I've listed above. Cheers.

Answer 26

I got \[x ^{2}-9x+72\] for my final answer and for the values of x I got x=10.68 and x=-1.68

Answer 27

where did you get 72 from?

Answer 28

\[3\times -8\neq72\]

Answer 29

Sorry I meant 18, not sure how that got there

Answer 30

Good. Excellent.

Answer 31

Now, you have to check each answer to see if it works with the original equation.

Answer 32

Could you do that please and see if the negative answer works in the equation.

Answer 33

Use a calculator.

Answer 34

If it doesn't then, the negative answer is not a solution. Therefore you would only have one, since I'm sure the positive answer would work.

Answer 35

Yeah I get a math error for the negative answer

Answer 36

So therefore, it doesn't work. You will thus have one solution.

Answer 37

So you would put an arrow to the negative answer and write no solution. Then on the next line you write, therefore x=10.68

Answer 38

Or something similar to that.

Answer 39

Ok that makes sense, thanks for the help it is much appreciated

Answer 40

Is there a way to give a medal or something, I'm new here.

Answer 41

No worries. IF you need any clarification, you should ask your teacher for further information. Yes, there is, on he right hand side, it says best response. You can choose the person that helped you the most or gave you a good answer.

Answer 42

And I almost forgot that you were new here: Welcome to OpenStudy, feel free to ask anymore questions on here, if you feel you're stuck on something. Have fun and enjoy using this website properly and efficiently.

Answer 43

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