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 Exercise [05.11] 
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Joined: 22 May 2008, 19:08
Posts: 18
Post Exercise [05.11]
First of all we have that w=b^z=e^{z\log{b}} and z=\log_b{w}.

And so w=e^{z\log{b}}\Rightarrow\log{w}=z\log{b}\Rightarrow z=\frac{\log{w}}{\log{b}}\Rightarrow \log_b{w}=\frac{\log{w}}{\log{b}}

As w=w\cdot e^{2k\pi i}, then:

z=\log_b{w}=\log_b{(w\cdot e^{2k\pi i})}=\log_b{w}+\log_b{e^{2k\pi i}}=\log_b{w}+\frac{\log{e^{2k\pi i}}}{\log{b}}
z=\log_b{w}+\frac{2k\pi i}{\log{b}}


08 Jun 2008, 17:37
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