Logarithmic Proof (1)

Prove that:

\log _{ a }{ x=\frac { 1 }{ \log _{ x }{ a }  }  }

Proof:

\log _{ a }{ x } =p\\ \\ { a }^{ p }=x\\ \\ { x }^{ \frac { 1 }{ p }  }=a\\ \\ \log _{ x }{ a } =\frac { 1 }{ p } \\ \\ p\log _{ x }{ a } =1\\ \\ p=\frac { 1 }{ \log _{ x }{ a }  } \\ \\ As,\quad p=p:\\ \\ \log _{ a }{ x } =\frac { 1 }{ \log _{ x }{ a }  }

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