Could someone provide a solution to the equation $$ 3^x = 2x+3. $$
Our teacher told us to solve it graphically, but I was curious what the exact answers might be and just plugged it into Wolfram Alpha and saw that the two solutions came from the principle and the $-1$ branch of the Lambert $W$ function.
I am familiar with the "function" and how it is the inverse "function" of the function $xe^x$, but whatever transformations I tried I just couldn't obtain the wolfram alpha solution.
Any help, hints or even a solution is greatly appreciated.