How do I solve this?

Question

How do I solve this?

0

740

2

+117

0.5xlnx−1.5x=0

The correct answer is e³, however I don't understand how you get this number from the equation above.

Namodesto Oct 7, 2015

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#1

+6252

+10

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

Rom Oct 7, 2015

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Rom · Answer 1 · 2015-10-07T04:52:21

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

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Namodesto · Answer 2 · 2015-10-07T05:00:36

Thank you so much!!

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