Question

Log (x^2+y^2) =logx+logy+log2, show that x=y

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{log(x^2+y^2)=log\,x+log\,y+log\,2}$

$\underline{\textbf{To prove:}}$

$\mathsf{x=y}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{log(x^2+y^2)=log\,x+log\,y+log\,2}$

$\textsf{Using product rule of logarithm,}$

$\mathsf{log(x^2+y^2)=log(2xy)}$

$\mathsf{x^2+y^2=2xy}$

$\mathsf{x^2+y^2-2xy=0}$

$\mathsf{(x-y)^2=0}$

$\implies\mathsf{x-y=0}$

$\implies\boxed{\mathsf{x=y}}$

$\underline{\textbf{Find more:}}$

If 2log(x-y)=logx +logy, prove that 2log(x+y)= log5+logx +logy

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