Logs (1 Viewer)

[hscishard]

I think this is off topic for hsc maths for some reason

From what I've read, logax=y
a needs to be positive, thus x needs to be positive

What about equations like these

where a is positive. x and y can be either negative or positive.

I've done






ln(-1) isn't possible. If we don't use the absolute value thing(which I think you shouldn't in this case), we get an undefined y value. Though it's possible to find a real y value.

So is there some extension on the logs to find powers with negative bases?

 

[AAEldar]

Complex logs.

You can get this from the result and by taking logs, and that result is taken from which is taken from the Maclaurin Series expansion for sin and cos.

Someone correct me if I'm wrong D:

 

[hscishard]

Holy shit wtf lol

 

[cutemouse]

In complex analysis there are two types of logarithmic functions:

1) Normal logarithmic function (ie. log)
2) Principal logarithmic function (ie. Log)

By definition, log z = ln|z| + i arg z

and Log z = ln|z| + iArg z

Arg z is the principal argument, ie. -pi < Arg z <= pi

arg z = Arg z + 2 pi k, k integral

 

[hscishard]

ok
What uni maths is that?

 

[cutemouse]

That would be second year maths.

 

[Trebla]

I sometimes wish I had taken real/complex analysis but I'm an applied person...

 

[hscishard]

Why? What can it be used for in real life?

It doesn't look very interesting...but thats just me

 

[Shadowdude]

Why? What can it be used for in real life?

It doesn't look very interesting...but thats just me

gogo to applied maths, you applied maths person!