How to solve if x^2+y^2=10xy prove that 2log(x+y)=logx+logy+3log2. I have a maths problem to solve, can anyone drop a paper solution for if x^2+y^2=10xy prove that 2log(x+y)=logx+logy+3log2.
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if x^2+y^2=10xy prove that 2log(x+y)=logx+logy+3log2
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Solution for if x^2+y^2=10xy prove that 2log(x+y)=logx+logy+3log2 is given below
Given
X²+y² = 10xy
We know that
(x+y)² = x² + y² + 2xy
Substitute x²+y² = 10xy value in above Equation
(x+y)² = 10xy+2xy
(x+y) = 12xy
Apply Logarithm value on both side.
log (x+y) = log (12xy)
log (x+y) = log (3 * 4 * xy) +0
We know log a power m= m log a
log(ab) = loga + log b
Apply above rules to Equation
log (x+y)² = log (3 * 4 * xy)
2log (x+y) = log(xy) + log3+ loge
2log (x+y)= log x+logy + log 3 + log 2 square
2log (x+y) = log x + logy + log3 + 2log 2
2log (x+y) = log x+ logy + 2log2 + log 3
If you want a clear solution for the above maths problem refer below image.