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Mathematics 36 Online
OpenStudy (anonymous):

what is the solution to 2e^x-5=1

OpenStudy (anonymous):

does anyone know this?

OpenStudy (zepp):

Of course, there must be someone who understand this question!

OpenStudy (zepp):

Can you isolate \(\large (e^x)\) first?

OpenStudy (anonymous):

Umm get ride of the 5?

OpenStudy (zepp):

Can you show me what you did?

OpenStudy (anonymous):

\(2e^{x-5} = 1\) is this the question??

OpenStudy (anonymous):

the minus 5 isnt a exponent

OpenStudy (zepp):

Ah

OpenStudy (anonymous):

Okay.. \(2e^{x} -5= 1\) right??

OpenStudy (zepp):

\[\large e^{x-5}=\frac{1}{2}\]

OpenStudy (anonymous):

Yes

OpenStudy (anonymous):

Wait zepp question is not that..

OpenStudy (zepp):

>.>

OpenStudy (anonymous):

1/2 isnt correct

OpenStudy (zepp):

That's what I though at first, now you all confused me!

OpenStudy (anonymous):

Add 5 both the sides first

OpenStudy (anonymous):

Okk

OpenStudy (zepp):

\[\large 2e^x-5=1\]Isolate \(e^x \) first

OpenStudy (anonymous):

And show me what you get.. @kaylee177

OpenStudy (zepp):

Wrong tag :P

OpenStudy (anonymous):

2e^x=6?

OpenStudy (zepp):

Correct, now isolate e^x by eliminating the 2, what you should do?

OpenStudy (anonymous):

Divide by 2..

OpenStudy (anonymous):

divide?

OpenStudy (zepp):

Yep yep

OpenStudy (anonymous):

Zep Zep

OpenStudy (anonymous):

ok um e^x=3?

OpenStudy (anonymous):

Yes going right..

OpenStudy (anonymous):

Now guess How can you find x ??

OpenStudy (anonymous):

i have no idea...

OpenStudy (anonymous):

x is in the power so you have to use Logarithm here..

OpenStudy (anonymous):

Take natural log both the sides: \[\large \ln(e)^x = \ln(3)\]

OpenStudy (anonymous):

Getting this point??

OpenStudy (zepp):

Or, \(\large \log_e\omega=\ln\omega\)

OpenStudy (anonymous):

Now there is one power rule you have to remember that: \[\large \color{green}{\ln(x)^a = a \cdot \ln(x)}\]

OpenStudy (anonymous):

Sorry I forgot to add base so: \[\large \ln_e(e)^x = \ln_e(3)\]

OpenStudy (zepp):

@waterineyes Wouldn't \(\large e^x=3\\\large \log_e{3=x}\) a little bit faster?

OpenStudy (anonymous):

So from there Zepp what do I do?

OpenStudy (anonymous):

I am explaining how you get x only where e gone??

OpenStudy (anonymous):

Ok, I'm trying to get x

OpenStudy (anonymous):

By applying that formula I have written in green: \[\large x \cdot \ln_e(e) = \ln_e(3)\]

OpenStudy (anonymous):

Remember: \[\large \color{blue}{\ln_e(e) = 1}\]

OpenStudy (anonymous):

Or you can say that: \[\large \color{blue}{\ln_a(a) = 1}\] a can be anything..

OpenStudy (anonymous):

so once you do that, whats the answer?

OpenStudy (anonymous):

So you will get now: \[\large x(1) = \ln_e(3)\] \[x = \ln_e(3)\]

OpenStudy (anonymous):

Do you know the value of \(ln_e(3)\) ??

OpenStudy (anonymous):

No what is it?

OpenStudy (zepp):

o.o

OpenStudy (anonymous):

\[\ln_e(3) = 1.0986\]

OpenStudy (anonymous):

Do you know the base of ln @Herp_Derp

OpenStudy (anonymous):

Ok thanks so much! I have more questions, please be here! lol

OpenStudy (anonymous):

I am just showing @kaylee177 he is a beginner for logs..

OpenStudy (anonymous):

No need...

OpenStudy (anonymous):

She lol she is a beginner

OpenStudy (anonymous):

I always when used he the reply comes she.. I made callisto he..

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