Suppose you have the equation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x^2*(log x)^{1/3}=-C [/tex]

for very small C. I have a book claims that asymptotically, for very small C, the solution is:

[tex]x^2=C*\frac{2}{[logC]^{1/3} } [/tex]

I'm not quite sure how to show this. If the 2 wasn't there, it looks like what they did was:

[tex]x^2=-\frac{C}{(log x)^{1/3}} [/tex]

and just substituted -C for x on the RHS:

[tex]x^2=\frac{C}{(log C)^{1/3}} [/tex]

I was thinking maybe you could substitute -C for x^{2}instead to get:

[tex]x^2=\frac{2^{1/3}C}{(log C)^{1/3}} [/tex]

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# Solving a transcendental equation

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