Question

1. Compute log25(9).log8(27)​

Answer 1

SOLUTION

TO DETERMINE

$\sf{ log_{25}(9). log_{8}(27) }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

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

$\displaystyle \sf{2. \: \: \: log_{x}( {y}^{n} ) = n log_{x}(y) }$

EVALUATION

$\displaystyle \sf{ log_{25}(9) . log_{8}(27) }$

$\displaystyle \sf{ = \frac{ log(9) }{ log(25) } \times \frac{ log(27) }{ log(8) } }$

$\displaystyle \sf{ = \frac{ log( {3}^{2} ) }{ log( {5}^{2} ) } \times \frac{ log( {3}^{3} ) }{ log( {2}^{3} ) } }$

$\displaystyle \sf{ = \frac{2 log( 3 ) }{ 2log( 5) } \times \frac{3 log( 3 ) }{3 log( 2 ) } }$

$\displaystyle \sf{ = \frac{ log( 3 ) }{ log( 5) } \times \frac{ log( 3 ) }{ log( 2 ) } }$

$\displaystyle \sf{ = log_{5}(3). log_{2}(3) }$

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