Question

(log 4 to the base 3)(log 81 to the base 4)

Answer 1

SOLUTION

TO DETERMINE

$\sf{ log_{3}(4) \times log_{4}(81) }$

FORMULA TO BE IMPLEMENTED

$\displaystyle \sf{ 1. \: \: log_{x}(x ) = 1 }$

$\displaystyle \sf{ 2. \: \: log_{x}(y ) = \frac{ log(y) }{ log(x) } }$

EVALUATION

$\sf{ log_{3}(4) \times log_{4}(81) }$

$\displaystyle \sf{ = \frac{ log(4) }{ log(3) } \times \frac{ log(81) }{ log(4) } } \: \: (by \: formula \: 2)$

$\displaystyle \sf{ = \frac{ log(81) }{ log(3) } }$

$\displaystyle \sf{ = log_{3}(81) }$

$\displaystyle \sf{ = log_{3}( {3}^{4} ) }$

$\displaystyle \sf{ = 4 \times log_{3}(3 ) }$

$\displaystyle \sf{ = 4 \times 1 }$

$= 4$

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