اگر ${\log ^۲} = a$ باشد مقدار عبارت $A = {\log ^{۰/۲۵}} \times {\log ^{\frac{{\sqrt ۲ }}{۲}}}$ کدام است؟
${\log ^2} = a$$\left\{ {\begin{array}{*{20}{c}}{{{\log }^{0/25}} = {{\log }^{\frac{{25}}{{100}}}} = {{\log }^{\frac{1}{4}}}}\\{{{\log }^{\frac{{\sqrt 2 }}{2}}} = {{\log }^{{{\frac{2}{2}}^{\frac{1}{2}}}}} = {{\log }^{{2^{\frac{1}{2} - 1}}}}}\end{array}} \right.$$\left\{ {\begin{array}{*{20}{c}}{ = {{\log }^{\frac{1}{{{2^2}}}}} = {{\log }^{{2^{ - 2}}}} = - 2{{\log }^2} = - 2a}\\{ = {{\log }^{{2^{\frac{1}{2}}}}} = - \frac{1}{2}{{\log }^2} = - \frac{1}{2}a\,\,\,\,\,\,\,\,\,\,}\end{array}} \right.$$A = - 2a \times - \frac{1}{2}a = {a^2}$