Number of roots of equation

Question

I have to calculate number of roots of the quation $6\ln(x^2+1)=e^x$. $(6\ln(x^2+1) - e^x)^{'} = \frac{12x}{x^2+1} - e^x$. It's not easy to examine sign of $\frac{12x}{x^2+1} - e^x$. So, what should I do?

Answer 1

Hint: plot the graph of $y=6\log(x^2+1)$ and the graph of $y=e^x$ and look at the common points.