Question

Solve exactly and make sure to check all solutions:
2LN(x) = LN(2) + LN(3x - 4)
x = ?

Answer 1

ln(x^2) = ln(2(3x-4))

Can u do it now?

Answer 2

No I apologize still grasping concepts on logs

Answer 3

Everything else I have done relatively well on until now.

Answer 4

Think...Does it matter what ln is?

Answer 5

Pretend it was 2...

Answer 6

format it in x^2 - 6x - 8 = 0 ?

Answer 7

Yup.

Answer 8

The tricky bit is to get it here

ln(x^2) = ln(2(3x-4)) from what u had in your question.

Answer 9

so let me see if I followed what you did

Answer 10

the LN's are basically like terms correct?

Answer 11

so you combined the second two

Answer 12

actually it is x^2 - 6x + 8

Answer 13

so x = 4 or 2

Answer 14

Here are some of the rules for ln's (natural logarithms)(or logs in general).
log(xy) = log x + log y
log(x/y) = logx - log y
log x^p = p log x

Answer 15

aha that helps to get to the first part you solved

Answer 16

and the other....

Answer 17

the first one....

Answer 18

? sorry not understanding what you are asking

Answer 19

I wasn-t asking u anything, I was explaining that I used the first rule as well as the third.

Answer 20

oh alright I understand... thank you

Answer 21

so the final answer is simply 4 and 2?

Answer 22

If that's the solutions to the quadratic, yes.

Answer 23

beautiful... the Natural logs throw me off

Answer 24

you have been a huge help... better then my actual teacher. Been eons since I have been in school

Answer 25

U will need to understand them better when u get further in maths, better do some more studying.

Answer 26

yes been way too long... and have to do some Calc for my CS degree

Answer 27

Definitely need to understand them before u do calc or u will be in trouble

Answer 28

So to make sure I understand. On 7 + 3ln(x) = 6

Answer 29

Ah, this is different...

Answer 30

I wouls change it to 3ln(x) = 6 - 7
so
3ln(x) = -1

Answer 31

Then divide by 3 to get ln(x) = -1/3

Answer 32

Then lost due to ln again lol

Answer 33

No! Use rule 3.

Answer 34

oh then back up

Answer 35

3 ln x = ln x^3

Answer 36

okay yes as you pointed out in rule #3. So x^3 = -1

Answer 37

U could do what you said, this is easier.

Answer 38

No! Again!

You only have ln on one side not both.

Answer 39

So you can't just drop it.

Answer 40

or cancel it..

Answer 41

if you could hear how angry at myself I am right now you would appreciate it. Again been too long so your patience is incredible

Answer 42

This is why you need to understand what a log (and especially a natural log) is.

U have ln x^3 = -1 and now u have to "exponentiate" both sides...

Answer 43

By that I mean raise them to the power of e.

Answer 44

which from what a vaguely remember is a ridiculous long number

Answer 45

So u get

e^(ln x^3) = e^-1

Answer 46

Now e^(ln x^3) = x^3 (by definition of the natural logarithm).

Answer 47

okay

Answer 48

So you end up with x^3 = e^-1 which u solve for x.

Answer 49

ah wouldn't it be then x = e^ - 1/3 ?

Answer 50

The key thing u need to understand is that

x = log to the base a of y MEANS y = a^x (ie the log is the inverse of the exponential).

In the case of natural logs, the base is e.

Answer 51

"ah wouldn't it be then x = e^ - 1/3 ?"

Yes, this is just a calculation.

Answer 52

To finish, you really do have to get comfortable with this....

Answer 53

you have been incredible

Answer 54

yes that is why I need to keep practicing

Answer 55

Right, do lots of examples till u can do it on autopilot....

Answer 56

actually been doing quite well in class... until these logs

Answer 57

Good luck!

Answer 58

Thank you estudier! hope to see you around again if I need help lol you have been awesome

Answer 59

np anytime.