Answer:
[tex]b^{\log_{b}n }=n[/tex]
Step-by-step explanation:
we are given
[tex]b^{\log_{b}n }[/tex]
Let [tex]b^{\log_{b}n } =y[/tex]
[tex]y= b^{\log_{b}n }[/tex]
taking log on both hand sides
[tex]\log y = \log (b^{\log_{b}n })[/tex]
[tex]\log y = {\log_{b}n} \log b[/tex]
[tex]{\log_{b}n}=\frac{\log n}{\log b}[/tex]
[tex]\log y=\frac{\log n}{\log b}\times \log b[/tex]
[tex]\log y = \log n[/tex]
[tex]y=n[/tex]
Hence our expression is equal to n
