Question

Log 3 base 4 * log 4base 3 + log 32 base 2

Answer 1

$\huge{ \boxed{ \underline{ \underline{ \red{ \bf{Given}}}}}}$

• log4(3) × log3(4) + log2(32)

$\large{ \boxed{ \underline{ \underline{ \pink{ \bf{Properties \: To \: Be \: Used :-}}}}}}$

$\begin{gathered} \\ \quad \implies \quad \rm \dfrac{1}{ log_{b}(a) } = log_{a}(b) \\ \end{gathered}$

$\begin{gathered} \\ \quad \implies \quad \sf log_{a}( {b}^{c} ) = c \times log_{a}(b) \\ \end{gathered}$

$\begin{gathered} \\ \quad \implies \quad \sf log_{a}(a) = 1 \\ \end{gathered}$

$\huge{ \underline{ \underline{ \green{ \sf{Calculation :-}}}}}$

$\\ \quad \implies \quad \rm log_{4}(3) \times log_{3}(4) + log_{2}(32)$

$\\ \quad \: \: \: \: \: \: \: \: \: \implies \quad \rm\dfrac{1}{ \cancel{ log_{3}(4)} } \times \cancel{log_{3}(4)} + log_{2}( {2}^{5} )$

$\\ \quad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \quad \rm 1 + 5 \times log_{2}(2)$

$\\ \quad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \quad \rm1 + 5(1)$

$\\ \quad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies \quad \sf 1 + 5$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large\implies{ \boxed{ \bf{ \purple{6}}}}$

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Answer 2

Answer:

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