Logarithmic Equation: Solve (1/x)^{2 - 3 ln(x)} = (1/e) * x^{1 + ln(x)}

[IloveIl]

Can you help me solve this:

. . . . .\(\displaystyle \large{ \left(\dfrac{1}{x}\right)^{2 - 3 \ln(x)}\, =\, \dfrac{1}{e}\, \cdot\, x^{1 + \ln(x)} }\)

I don't know how to get rid of the 1/e.

Thanks

 

[stapel]

Can you help me solve this:

. . . . .\(\displaystyle \large{ \left(\dfrac{1}{x}\right)^{2 - 3 \ln(x)}\, =\, \dfrac{1}{e}\, \cdot\, x^{1 + \ln(x)} }\)

I don't know how to get rid of the 1/e.

The 1/e is just a number, like 2 or \(\displaystyle \pi.\) There is no need to "get rid of" it.

What have you done toward solving this? For instance, you noted that the logs are "of x" so, on the left-hand side, what did you do in order to get a base of just x? What did you do with the fact that ln(x) = log_x (x)/log_x(e)? And so forth.

Please be complete. Thank you!