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Find ‘x’ which satisfy the equation. log 3 x log 4 x (log 5 x – 1) = log 5 x (log 4 +log 3 x )

Find ‘x’ which satisfy the equation.
 
log3xlog4x(log5x – 1) = log5x(log4+log3x)

Grade:9

1 Answers

noogler
489 Points
9 years ago
x=60
 
(logx/log3 )(logx/log4 )(logx/log5-1)=logx/log5(logx/log4+logx/log3)                               here logx means logex
(logx/log3 )(logx/log4 )(logx-log5/log5)=logx/log5(log3logx+log4logx/log3log4)
(logx)2(logx-log5)=logx(log3logx+log4logx)
(logx)2(logx-log5)=(logx)2(log3+log4)
logx-log5=log3+log4
logx=log3+log4+log5
logx=log(3x4x5)                    loga+logb+logc=log(abc)
logx=log60
x=60

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