Exercise ID331

Algebra → Logarithm → Logarithm equations
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Evaluate the following expression:

logx3+log3x=logx3+log3x+12

1log3x+log3x=1log3x12+log3x12+12 1log3x+log3x=112log3x+12log3x+12 log3x=t 1t+t=2t+12t+12 /×2t 2+2t2=4-t2+t 2+2t2-4+t2-t=0 t2-t-2=0 t1,2=1±1+82 t1,2=1±32 t1=2 t2=-1 log3x=2 x=32x=9 log3x=-1 x=3-1x=13
x=3-1x=13
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