if x^2+y^3=25xy then prove that 2log(x+y)=3log3+logx+logy
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Correction in question, y² is written wrong as y³
===============
Solution,
LHS
2log(x + y)
=> log(x +y)²
=> log(x²+y²+2xy)
=> log(25xy + 2xy)
=> log27xy
-----------------
RHS
3log3 + logx + logy
=> log3³ + logx + logy
=> log27 + logx +logy
=> log(27×x ×y)
=> log27xy
Hence, log27xy = log27xy
LHS = RHS
I hope this will help you
(-:
===============
Solution,
LHS
2log(x + y)
=> log(x +y)²
=> log(x²+y²+2xy)
=> log(25xy + 2xy)
=> log27xy
-----------------
RHS
3log3 + logx + logy
=> log3³ + logx + logy
=> log27 + logx +logy
=> log(27×x ×y)
=> log27xy
Hence, log27xy = log27xy
LHS = RHS
I hope this will help you
(-:
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