Exercise ID330

Algebra → Logarithm → Logarithm equations
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Evaluate the following expression:

xlog3x-1=3

xlog3x-1=3 /log33 F: x>0 log3xlog3x-1=log33 log3x-1×log3x=1 log3x-1×log3x12=1 log3x-1×12log3x=1 log3x=t t-1×12t=t 12t2-12t=1 12t2-12t-1=0 /×2 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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