solve the following for x ln(x)+2=-3ln(x)+10?

ln(x) + 2 = -3ln(x) + 10

ln(x) + 3ln(x) + 2 = 10 // adding 3ln(x) to each side
4ln(x) + 2 = 10 // simplfying left hand side
4ln(x) = 8 // subtracting 2 from each side
ln(x) = 2 // dividing each side by 4

x = e^2 // taking inverse natural logarithm

ln x + 3 ln x = 8
4 ln x = 8
ln x = 2
x = e ²

ln(x) + 2 = -3ln(x) + 10
ln(x) + 3ln(x) = -2 + 10
ln(x) + ln(x^3) = 8
ln(x^4) = 8
4ln(x) = 8
ln(x) = 8/4
ln(x) = 2
x = e^2

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I dunno