e^(3x)=x

Look at the graph : https://www.desmos.com/calculator/ijwc1arqf6

Note that there is no intersection point .......thus.......no solutions......!!!!

${e}^{3x}=x$

${e}^{3x}≠x$

$ln({e}^{3x})≠ln(x)$

$3x\times ln(e)≠ln(x)$

$3x≠ln(x)$

$x≠\frac{ln(x)}{3}$