উদাহরণ ২৷
প্রমান করো [tex]{\log _2}10 - {\log _8}125 = 1[/tex] [H.S '90]
প্রমান:
[tex]\begin{array}{l}
{\log _2}10 - {\log _8}125\\
= {\log _2}\left( {2 \times 5} \right) - {\log _8}{5^3}\\
= {\log _2}2 + {\log _2}5 - 3{\log _8}5\\
= 1 + {\log _2}5 - 3\frac{1}{{{{\log }_5}8}}\\
= 1 + {\log _2}5 - 3\frac{1}{{{{\log }_5}{2^3}}}\\
= 1 + {\log _2}5 - 3\frac{1}{{3{{\log }_5}2}}\\
= 1 + {\log _2}5 - \frac{1}{{{{\log }_5}2}}\\
= 1 + {\log _2}5 - {\log _2}5\\
= 1\left( {proved} \right)
\end{array}[/tex]
