Can someone help me solve this please?

Question

I have a problem that I'm stuck on and if anyone is willing to help me, that would be awesome.

Solve for x: (logarithms)

2e^2lnx=18

I've simplified it down to:

2 ln (18) = 2 ln (x)

Then divided both sides by 2 to get:

ln 18 = ln x

Is this right or what should I have done right?

Answer 1

If I'm reading correctly what you've typed, you didn't take logs correctly in the second line.  

First line:

2*(e^2)*lnx = 18                                                                           (line 1)

Second line: It would seem that you took logs to get ln (18).  But if you take logs of the first line, you get:

ln (2 (e^2) lnx) = ln (18)                                                                 (line 2)

which is NOT helpful because you'll end up with a ln(ln(x)) expression!

Instead, use what you know from basic algebra: Completely isolate the term you're interested in, namely ln x.  Hint: You don't need to take logs.  

Or did you actually mean to state your problem as

2*e^{2 ln x} = 18?                                                                         (line 3)

In that case, you're still wrong.  Fully simplify (line 3)--remember the relationship between e and ln--and you'll immediately get an answer for x.

In good conscience, I have a feeling I'm not supposed to give you the answer, though.

Answer 2

Zero

Answer 3

2e^2lnx=18

e^2 ln (x) =9

ln (x) = 9 / e^2

x = e^[9/e^2]

9 / e^2 = 1.2180175

e^[9/e^2] = 3.380479

Answer 4

Then,Lnx=18/2e^2=1.218=Ln3.38,x=3.38

======================================...

CHECK:2e^2Ln 3.38 =2e^2 (1.218)=18

Answer 5

From the equation, we get

e^2lnx = 18 / 2 = 9

Now, 2 lnx can also be written as ln(x^2)

So, e^2lnx = e^ln(x^2) = 9

Taking natural log on both the sides,

ln(x^2) = ln 9

or x^2 = 9

or x  = 3

Hope it is clear