I Can't Seem To Isolate $x$ !

Algebra Level 3

Solve the following equation for all real values of $x$ .

$e^{x} - e^{-x } = 5$

\ln \left( \frac{5\pm\sqrt{21}}{2}\right)

\ln \left( \frac{5+\sqrt{21}}{2}\right)

\ln \left( \frac{5-\sqrt{29}}{2}\right)

\ln \left( \frac{5\pm\sqrt{29}}{2}\right)

\ln \left( \frac{5+\sqrt{29}}{2}\right)

\ln \left( \frac{5-\sqrt{21}}{2}\right)

1 solution

Rishabh Jain
Feb 23, 2016

$\large e^{x} - e^{-x } = 5$ $\large \implies e^{2x}-5e^x-1=0$ $\large \implies e^x=\dfrac{5+\sqrt{29}}{2}$ Note that we have dropped $\dfrac{5-\sqrt{29}}{2}$ since the range of $e^x$ function is $\mathbb{R^+}$ and $\dfrac{5-\sqrt{29}}{2}<0$ . $\Large \implies x=\huge\color{#456461}{\boxed{\color{#D61F06}{\boxed{\color{#007fff}{ \ln (\dfrac{5+\sqrt{29}}{2})}}}}}$

Nice solution!

PS 29 is my roll no. :P

Nihar Mahajan - 5 years, 3 months ago

Rishabh Jain - 5 years, 3 months ago

Mine 27 :-)

Department 8 - 5 years, 3 months ago

mine too 27

Kaustubh Miglani - 5 years, 3 months ago

am i like the only who used hyperbolic sin and arc hyperbolic sin identities?

Karish Thangarajah - 5 years, 3 months ago

Nope, I saw someone who used that as well. Pretty good way to solve the problem if you ask me.

Kenneth Choo - 5 years, 3 months ago

Same solution.

@Rishabh Cool Can I request something? Please change your Display picture :P

@Hobart Pao , This was the first problem of yours I solved :P

Mehul Arora - 5 years, 3 months ago

@Mehul Arora Поздраляю! I'm sure you could do more, but only if you're interested.

Hobart Pao - 5 years, 3 months ago

Yes, I will try for sure :P

Mehul Arora - 5 years, 3 months ago

Why ?? Any reason?? (coz I'm a big WWE fan :-} )

Rishabh Jain - 5 years, 3 months ago

Yes. There is a reason. I hate WWE. Way too much

I liked the earlier display pic of yours. That Sigma.

Mehul Arora - 5 years, 3 months ago

@Mehul Arora – OK... Done :-)

Rishabh Jain - 5 years, 3 months ago

@Rishabh Jain – Great! Thanks :D

Mehul Arora - 5 years, 3 months ago

Same here I am also a bigggg wwe fan.

@Tanishq Varshney @Lakshya Sinha are also big wwe fans I think.

Harsh Shrivastava - 5 years, 3 months ago

@Harsh Shrivastava – Oh damn yes!!

Department 8 - 5 years, 3 months ago

@Department 8 – Have you watched the latest RAW episode ? ( in which HHH screwed Roman!!)

Rishabh Jain - 5 years, 3 months ago

@Rishabh Jain – Yes I felt bad

Department 8 - 5 years, 3 months ago

@Department 8 – What HHH did was totally wrong (my thoughts )..... and I'm sure in next episode of RAW he'll definitely pay the price !! :-}

Rishabh Jain - 5 years, 3 months ago

I Can't Seem To Isolate x x x !

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I Can't Seem To Isolate $x$ !