Question

​5) Resolva o logaritmo Log 81 x=¼​

Answer 1

​5) Resolva o logaritmo

Log 81 x=¼​

X = 81 ^ 1/4

X = (3^4)^1/4

X = 3^4/4

X = 3

Answer 2

$\boxed{\begin{array}{l}\sf Resolva~o~logaritmo~\log_{81}x=\dfrac{1}{4}.\\\underline{\sf soluc_{\!\!,}\tilde ao:}\\\rm Lembre-se~que~\log_ba=x\iff b^x=a\\\rm desde~que~a>0~e~1\ne b>0.\\\rm Portanto~\log_{81}x=\dfrac{1}{4}\iff x=81^{\frac{1}{4}}\\\begin{array}{c|c}\rm81&\rm3\\\rm27&\rm3\\\rm9&\rm3\\\rm3&\rm3\\\rm1\end{array}\\\rm 81=3^4\\\rm DA\acute I:\\\rm x=(3^4)^{\frac{1}{4}}\\\rm recordando~a~propriedade~(a^m)^n=a^{m\cdot n}\\\rm x=3^{\backslash\!\!\!4\cdot\frac{1}{\backslash\!\!\!4}}\\\rm x=3^1\\\rm x=3\\\rm ou~seja,\log_{81}x=\dfrac{1}{4}\iff x=3\end{array}}$