



 
Hi Mike, I wasn't sure what was meant by "touch each other" so I plotted the two functions \[f(x) = \ln(x) + \frac{1 + \ln(2)}{2} \mbox{ and } g(x) = x^{2}.\] It does look like the two curves have a common tangent at approximately x = 0.7. If they do have a common tangent there then at this point we would have \[f^\prime (x) = g^\prime (x).\] Can you finish it? 



Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 