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## Homework Statement

The relationship between arctanh and log is:

arctanh(x)=[itex]\frac{1}{2}log(\frac{1+x}{1-x})[/itex]

but if i take x=1.5,

I have:

arctanh(1.5)=0.8047 + 1.5708i

and

[itex]\frac{1}{2}log(\frac{1+1.5}{1-1.5})[/itex]=0.8047 + 1.5708i

as expected, but using the laws of logarithm, why does this not equal to:

[itex](\frac{1}{2})\frac{1}{2}log((\frac{1+1.5}{1-1.5})^2)[/itex]=0.8047

?

## Homework Equations

## The Attempt at a Solution

Thank you in advance