উদাহরণ ১৪৷ 
হলে দেখাও যে
[H.S ‘88]
প্রমান:
{a^4} + {b^4} = 14{a^2}{b^2}\\
\Rightarrow {a^4} + 2{a^2}{b^2} + {b^4} = 16{a^2}{b^2}\\
\Rightarrow {\left( {{a^2} + {b^2}} \right)^2} = 16{a^2}{b^2}\\
\Rightarrow {a^2} + {b^2} = 4ab \to \left( 1 \right)
\end{array}" alt="\begin{array}{l}
{a^4} + {b^4} = 14{a^2}{b^2}\\
\Rightarrow {a^4} + 2{a^2}{b^2} + {b^4} = 16{a^2}{b^2}\\
\Rightarrow {\left( {{a^2} + {b^2}} \right)^2} = 16{a^2}{b^2}\\
\Rightarrow {a^2} + {b^2} = 4ab \to \left( 1 \right)
\end{array}"/>
অতএব
{\log _e}\left( {{a^2} + {b^2}} \right)\\
= {\log _e}\left( {4ab} \right)\left[ {by\left( 1 \right)} \right]\\
= {\log _e}a + {\log _e}b + {\log _e}4\\
= {\log _e}a + {\log _e}b + 2{\log _e}2\left( {proved} \right)
\end{array}" alt="\begin{array}{l}
{\log _e}\left( {{a^2} + {b^2}} \right)\\
= {\log _e}\left( {4ab} \right)\left[ {by\left( 1 \right)} \right]\\
= {\log _e}a + {\log _e}b + {\log _e}4\\
= {\log _e}a + {\log _e}b + 2{\log _e}2\left( {proved} \right)
\end{array}"/>