Question

The value of
$\frac{1}{ log_{6}(24) } + \frac{1}{ log_{12}(24) } + \frac{1}{ log_{8}(24) }$
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Answer 1

Answer:

2

Step-by-step explanation:

$\frac{1}{ log_{6}(24) } + \frac{1}{ log_{12}(24) } + \frac{1}{ log_{8}(24) }$

= log 6 base 24 + log 12 base 24 + log 8 base 24

= log ( 6x12x8 ) base 24

= log ( 2x3x3x4x4x2 ) base 24

= log ( 2x3x4 )² base 24

= log ( 24)² base 24

= 2 log ( 24) base 24

= 2(1) ( since log a base a = 1 )

= 2