Respuesta :
Answer:
[tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]
[tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex] = [tex]{{$log_{nb} \left(x\right)$}}[/tex]
Step-by-step explanation:
i) [tex]$\log_{nb} x[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( 1 + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex]
ii) therefore simplifying i) we get
[tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(b\right)}} + {{log_{b} \left(n\right)}})[/tex] = [tex]{{$log_{b} \left(x\right)$}}\div( {{log_{b} \left(nb\right)}})[/tex] = [tex]{{$log_{nb} \left(x\right)$}}[/tex]
iii) Hence the equation is proved.
