Logarithmic Proof (3)

Prove that:

\log _{ a }{ \left( { a }^{ n } \right) =n\log _{ a }{ (a) }  }

Say that:

{ a }^{ n }=p

Therefore:

\log _{ a }{ p=n }

So:

\log _{ a }{ \left( { a }^{ n } \right)  } \\ \\ =\log _{ a }{ \left( p \right)  } \\ \\ =\log _{ a }{ \left( p \right)  } \cdot 1\\ \\ =\log _{ a }{ \left( p \right) \cdot \log _{ a }{ \left( a \right)  }  } \\ \\ =n\cdot \log _{ a }{ \left( a \right)  }

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