Question

Log 27 base 3 .log 3 base 7 .log 7 base 81

Answer 1

$\sf \rightarrow \quad log_{3} 27 \cdot log_{7}3 \cdot log_{81}7 \\ \\ \sf \rightarrow \quad 3 \cdot \frac{ log_{3}3 }{ \cancel{ log_{3}7 } } \cdot \frac{ \cancel{ log_{3}7} }{ log_{3}81 } \\ \\ \sf \rightarrow \quad 3 \cdot 1 \cdot \frac{1}{4} \\ \\ \sf \rightarrow \quad \frac{3}{4} \\ \\ \\ \sf \: \: \underline{Properties \: used:} \\ \\ \qquad \rightarrow \sf log_{b}a = \frac{ log_{m}a }{ log_{m}b } \\ \\ \qquad \rightarrow \sf log_{a}a = 1$

Answer 2

$\huge \sf{ \underline{ \color{olive}{Solution}}}$

$\sf { \pink{\longrightarrow \quad log_{3} 27 \cdot log_{7}3 \cdot log_{81}7 }}\\ \\ \sf{ \pink{\longrightarrow \quad 3 \cdot \frac{ log_{3}3 }{ \cancel{ log_{3}7 } } \cdot \frac{ \cancel{ log_{3}7} }{ log_{3}81 }}} \\ \\ \sf {\pink{\longrightarrow \quad 3 \cdot 1 \cdot \frac{1}{4}}} \\ \\ \sf{\red{\longrightarrow \quad \frac{3}{4}}}$

$\begin{gathered}\small\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \sf \underline{ \purple{{Properties \: used:}}} \\ \\ \implies \sf log_{b}a = \frac{ log_{m}a }{ log_{m}b } \\ \\\implies \sf log_{a}a = 1{}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}$