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Question

If log10(2x+1)+2x=log106+xlog1050, then the value of x is

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Solution

log10(2x+1)+2x=log106+xlog1050
log10(2x+1)+2xxlog10(1002)=log106
log10(2x+1)+2xx(log10100log102)=log106
log10(2x+1)+2x2x+log102x=log106
log10[(2x+1)2x]=log106
2x(2x+1)=6
(2x)2+2x6=0
(2x+3)(2x2)=0
2x2=0 as 2x+30
x=1

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