Question

Hello! Please solve.​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

$\tt \:  ⟼\dfrac{1}{ log_{8}(6) } + \dfrac{1}{ log_{3}(6) } + \dfrac{1}{ log_{9}(6) }$

$\tt \:  = log_{6}(8) + log_{6}(3) + log_{6}(9)$

$\tt \:  \: \: \: \: \: \: \: \: \: \: \:  ✬ \: [ \because \: \dfrac{1}{ log_{x}(y) } = log_{y}(x) ]$

$\tt \:  = log_{6}(8 \times 3 \times 9)$

$\tt \:   ✬ \: [ \because \: log_{a}(x) + log_{a}(y) = log_{a}(xy)]$

$\tt \:  = log_{6}(216)$

$\tt \:  = log_{6}( {6}^{3} )$

$\tt \:  = \: 3 \: \: \: \: \: \: \: \: \: \: \: [ \because \: log_{a}( {a}^{x} ) = x ]$

$\large{\boxed{\boxed{\bf{Hence, \: \dfrac{1}{ log_{8}(6) } + \dfrac{1}{ log_{3}(6) } + \dfrac{1}{ log_{9}(6) } = 3}}}}$

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