Exercise ID329

Algebra → Logarithm → Logarithm equations
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Evaluate the following expression:

xlog10x+53=105+log10x

xlog10x+53=105+log10xlog1010 x13log10x+5=105+log10x1 x13log10x+5=105+log10x   log10() log10x13·log10x+5=log10105+log10x 13·log10x+5·log10x=5+log10x·log1010 13·log10x+5·log10x=5+log10x·1 log10x=t 13·t+5·t=5+t t+5·t=15+3t  t2+5t=15+3t  t2+5t-15-3t=0  t2+2t-15=0  t1,2=-2±22-4·1·-152 t1,2=-2±4+602=-2±642 t1,2=-2±82 t1,2=-1±4 t1=3 ; t2=-5 log10x1=3 x1=103=1000 log10x2=-5 x2=10-5=1105 x103,10-5
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