\(0.5 x \ln(x) -1.5 x = 0 \\ 0.5 x \ln(x) = 1.5 x \\ x \ln(x) = 3 x \\ \mbox{Since }\ln(0) \mbox{ is not defined }x \neq 0 \mbox{ and we can divide both sides by }x \\ \ln(x) = 3 \\ x = e^3\)
\(0.5 x \ln(x) -1.5 x = 0 \\ 0.5 x \ln(x) = 1.5 x \\ x \ln(x) = 3 x \\ \mbox{Since }\ln(0) \mbox{ is not defined }x \neq 0 \mbox{ and we can divide both sides by }x \\ \ln(x) = 3 \\ x = e^3\)
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