Question

if is x = log2(3) and y =log2(5) then express log2(60) in terms of x.y.
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Answer 1

check above solution...

Answer 2

SOLUTION

GIVEN

$\sf \: x = log_{2}(3) \: \: and \: \: y = log_{2}(5)$

TO DETERMINE

$\sf \: log_{2}(60) \: \: in \: terms \: of \: x \: and \: y$

EVALUATION

Here it is given that

$\sf \: x = log_{2}(3) \: \: and \: \: y = log_{2}(5)$

Now

$\sf \: log_{2}(60)$

$\sf \: = log_{2}(2 \times 2 \times 3 \times 5)$

$\sf \: = log_{2}( {2}^{2} \times 3 \times 5)$

$\sf \: = log_{2}( {2}^{2} ) + log_{2}( 3 ) + log_{2}( 5)$

$\sf \: = 2log_{2}( {2}^{} ) + log_{2}( 3 ) + log_{2}( 5)$

$\sf \: = 2 + x + y$

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