e^(3x)=x

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

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

\({e}^{3x}=x\)

\({e}^{3x}≠x\)

\(ln({e}^{3x})≠ln(x)\)

\(3x\times ln(e)≠ln(x)\)

\(3x≠ln(x)\)

\(x≠\frac{ln(x)}{3}\)