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Question

xlogx+74=10logx+1.

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Solution

Xlogx+74=10logx+1
logx+74=logx10(logx+1)
logx+74=(logx+1)logx
Let logx=t
t+74=t+1t
t2+7t=4t+4
t2+3t4=0
t2+4tt4=0
t(t+4)1(t+4)=0
t=1,4
logx=1,logx=4
x=101,104

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