The number of real roots of the equation

Let $\mathrm{e}^{\mathrm{x}}=\mathrm{t}>0$

$f(t)=t^{4}+2 t^{3}-t-6=0$

$f^{\prime}(t)=4 t^{3}+6 t^{2}-1$

$f^{\prime \prime}(\mathrm{t})=12 \mathrm{t}^{2}+12 \mathrm{t}>0$

$f(0)=-6, f(1)=-4, f(2)=24$

$\Rightarrow$ Number of real roots $=1$