Question 29899
Hi,

So *[tex \log\sqrt[3]{x}=\sqrt{\log x}]

The LHS can be rewritten as *[tex \frac{\log x}{3}=\sqrt{\log x}]

Now we can get rid of that nasty square root by squaring, but beware we might also introduce more solutions, so any answers we get at the end will have to be checked. *[tex (\log x)^2=9\log x].

We can now factorize, and solve for *[tex \log x]

*[tex (\log x)(\log x - 9)=0]. So either *[tex \log x=0] or *[tex \log x=9].

Now I don't know what base your logorthms are in, but I'm going to assume base 10. So we have either *[tex x=1] or *[tex x=1000000000]. If you put these back into the equation, I think you'll find they both work.

Hope that helps,
Kev