Question

0=2ln(x/4) + 1

I don't understand how to solve this problem. Thank you!

Answer 1

Wolfram is telling me \[x=\frac{ 4 }{ \sqrt(e) }\]

But I don't understand HOW to find this.

Answer 2

ok, what you want to do is isolate x onto one side or solve for x

Answer 3

starting with \[2 \ln(\frac{x}{4})+1=0\]

Answer 4

first we want to remove the 1 from the left side

this can be done by subtracting 1 to both sides, since 1-1 =0
so it will look something like \[2 \ln(\frac{x}{4})+1-1=0-1\]
\[2 \ln(\frac{x}{4})=-1\]

Answer 5

100% following. (I pretty much was stuck at:

\[\ln(x) = -\frac{ 1 }{ 2 } + \ln(4)\]

Which I think is correct that far.

Answer 6

er, i wouldnt do it like that

Answer 7

Oh ok, I figured I was making this more difficult. Haha, please continue I won't interrupt.

Answer 8

i would then divide by 2 from both sides\[\frac{2}{2} \ln(\frac{x}{4}) = \frac{-1}{2}\]
so
\[ \ln(\frac{x}{4}) = \frac{-1}{2}\]

Answer 9

then take both sides to be the power of the exponential function
since e^(lnx) = x

Answer 10

\[e^{\ln{\frac{x}{4}}}=e^\frac{-1}{2}\]
\[\frac{x}{4}=e^\frac{-1}{2}\]

Answer 11

omg, yep... I see it now thanks to you. I dunno why I was thinking x/4 couldn't do that...

Answer 12

now \[x^{\frac{-1}{2}} = \frac{1}{\sqrt{x}}\]

Answer 13

then we just multiply 4 to both sides and you should get the answer above

Answer 14

Thanks so much.

Answer 15

yup no prob