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Question

Solve the equation log(x)=logx2 (base is 10)

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Solution

log(x)=logx2
If logab exist b>0
Here we have, x>0
x<0
x2=x
log(x)=log(x)
log(x)=[log(x)]2
[log(x)]2log(x)=0
log(x)[log(x)1]=0
log10(x)=0,log10(x)1=0
10log10(x)=100,log10(x)=1
x=1,10log10(x)=101
x=1,x=10x=10

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