Question

If log sub b(3^b)=b/2,thenb=?

Answer 1

\[If log sub b (3^b)=b/2,then b=?\]

Answer 2

\[\large \log_{b}(3^b)=\frac{b}{2}\]


\[\large \frac{\log_{10}(3^b)}{\log_{10}(b)}=\frac{b}{2}\]


\[\large \frac{b*\log_{10}(3)}{\log_{10}(b)}=\frac{b}{2}\]


\[\large \frac{\log_{10}(3)}{\log_{10}(b)}=\frac{1}{2}\]


\[\large \frac{2*\log_{10}(3)}{\log_{10}(b)}=1\]


\[\large \frac{\log_{10}(3^2)}{\log_{10}(b)}=1\]


\[\large \frac{\log_{10}(9)}{\log_{10}(b)}=1\]


\[\large \log_{b}(9)=1\]


\[\large 9=b^1\]


\[\large 9=b\]


\[\large b=9\]