Understanding Logarithmic Identities in Differential Equations

[HeLiXe]

This is related to differential equations, but I think my question has more to do with log identities than DE.

I keep seeing equations like

1/8 lny = t + c

simplified to get the solution

y = ce^8t

but I am unsure of the identity being used to get 1/8 into the exponent as 8. I already understand how everything else is simplified, just not this part. Thanks!

 

[Pengwuino]

Just multiply both sides by 8 and exponentiate both sides.

The other way to see this would be that 1/8 ln(y) = ln(y^{{1}\over{8}})

 

[HeLiXe]

*facepalm* Thanks penguwino LOL

 

[Pengwuino]

That'll be $5

 

[HeLiXe]

I'll give you $25

I kept switching it over the entire semester and never understood why I was doing that loll. This is what happens when the "simple steps" are skipped in math -_-

 

[Pengwuino]

Tattoo the logarithmic identities to your forearm. It's far more useful then some rose or star

 

[Dr. Seafood]

^ But then to avoid being suspected of cheating, you'd have to wear full-sleeve shirts during your exams. And that sucks when your exams are seated outside during a heatwave :(

 

[HeLiXe]

Tattoo the logarithmic identities to your forearm. It's far more useful then some rose or star

I'll see if I can have them burned on my retina :D

And that sucks when your exams are seated outside during a heatwave :(

That is so sadistic! -_- Who would ever do such a thing to an innocent student?

 

[I like Serena]

I'll see if I can have them burned on my retina :D

Try to burn them behind your retinas.
That works even better! ;)

That is so sadistic! -_- Who would ever do such a thing to an innocent student?

Oh, standard trick to flush out not-so-innocent students.

 

[HeLiXe]

Try to burn them behind your retinas.
That works even better! ;)

If there was something behind my retinae it would work better