Mathematics
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OpenStudy (anonymous):
what is the solution to 2e^x-5=1
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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?
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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):
\[\large e^{x-5}=\frac{1}{2}\]
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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!
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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
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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
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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...
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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:
\[\large \color{green}{\ln(x)^a = a \cdot \ln(x)}\]
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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
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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:
\[\large x(1) = \ln_e(3)\]
\[x = \ln_e(3)\]
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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
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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..