Alg9.4.45

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If $a^2+b^2=6ab\,$ then show that $2\log a+b= \log a+\log b+3\log 2\,$

Adding 2ab on both sides to make the left hand side a perfect square

$a^2+b^2+2ab=8ab\,$

$(a+b)^2=8ab\,$

Applying logs on both sides,we get

$2\log(a+b)=\log 8+\log a+\log b\,$

$2\log(a+b)=3\log 2+\log a+\log b\,$

Main Page:Algebra:Logarithmic

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