Question

when solving for x in ln(x+5)+ln(x^2)=ln(6x) can one just divide both sides by ln to obtain x^2-5x+5?

Answer 1

Solve with some x and see......

Answer 2

The roots of the quadratic are 1/2 (5 plus/minus sqrt5) so if you calculate with those in the ln expression, you will see the answer to your question.

Answer 3

I'm afraid @Razzputin and @estudier, those answers are not correct.

Answer 4

Would you like me to help?

Answer 5

I agree that I could have just said no, if that's what u mean....:-)

Answer 6

@estudier, no, all I meant was that the answers I see are not right. I'm not sure what you're talking about?

Answer 7

The question is " can one just divide both sides by ln " ?

Answer 8

Poster did not ask for a solution.

Answer 9

On the left side, you should first apply the following property:\[\ln xy =\ln x +\ln y\]where both x and y are greater than zero.

Answer 10

I know he didn't ask for a solution and that's clearly not what I'm doing. But he obviously needs some kind of lesson to achieve some level of understanding because he wrongly believes that you can divide by ln which is NOT true.

Now I think that you are implying that my help is not needed here so that's fine. I'll leave. Sorry to have bothered you @estudier.

Answer 11

If @Razzputin asks for my help then I'll be more than happy to. Simply let me know. Good Luck!

Answer 12

I'm not implying anything, I am just explaining to you that my answer is not "incorrect" as you stated..-)

Answer 13

Would you like to see my explanation and why I believe that your answer is incorrect?

Answer 14

No, thank you.

Answer 15

sorry i disapeared im back now had to have lunch with my dad

Answer 16

@Razzputin, do you see the property I gave above?

Answer 17

yes i do. Once i use that then do i divide both sides?

Answer 18

ln(x^3+5x^2)=ln(6x)

x^3+5x^2-6x=0

Answer 19

NO! Can you please show me what you have after you apply the property so that I can guide you further? I just don't want to end up giving you the answer. I want to teach you, if you could please show me your first step. Oh I see you did! That's correct, now what do you think you should do next? Can you tell me?

Answer 20

OK, so what should you do next?

Answer 21

\[x(x ^{2}+5x-6)=0\]
x(x-1)(x+6)=0
x=0
x=1
x=-6

only x=1 is applicable as in logs x>0

Answer 22

Yes and now what?

Answer 23

lol NO! .... YES! confusion in the ranks ha ha.

Answer 24

Perfect! Only x = 1 is a valid solution. Do you now have a better understanding of how to solve these types of problems?

Answer 25

yup yhanks, i see now that i can only divide the two sides if only one ln is present on each after simplifying them

Answer 26

@Razzputin and @hartnn, thank you for the medal!

Answer 27

no prob u deserved it. Most ppl here just hand out the answer its anoying

Answer 28

just a side note when u got x^3+5x^2-6x=0 , did u say, u divide both sides ?? what by ln ??
*one cannot simply divide by ln on both side*, its like you are equating the argument of ln
lnA = ln B then A+B

Answer 29

A=B

Answer 30

If \[\ln f(x)=\ln g(x)\]then f(x) = g(x) as long as f(x) and g(x) are both greater than zero.

Answer 31

well i had ln(x^3+5x^2 )=ln(6x) so i dropped the ln

Answer 32

yeah, but u DID NOT DIVIDE by ln.....keep that in mind...

Answer 33

NO! dividing by ln is not allowed.

Answer 34

lol my bad, ha ha wrong terminology

Answer 35

If you have two logarithms to the same base that are equal, then you equate their arguments (antilogarithms), but it is wrong to say that you divide by ln. Understand?

Answer 36

yup thanks

Answer 37

Welcome! No need to even say thanks. I love teaching and I love math!