I understand about log and exponential equations/functions, but I can't solve these (the numbers are just examples, of course):
$ 4^x = x + 10$
$x^x = 3$
$(2x + 3x^2)^{x + 1} = (x - x^3)^{x^2}$
Are there specific algebraic steps that I can follow so that I solve them? Or, if not, what are the other means to find $x$ in each?
Start reading. The second problem is solved here. As for the first one, here it goes:
$$4^x=x+10\quad|\cdot(-1)\cdot4^{-(x+10)}\iff-4^{-10}=-(x+10)\cdot4^{-(x+10)}\quad|\cdot\ln4\iff$$
$$-4^{-10}\ln4=-(x+10)\ln4\cdot e^{-(x+10)\ln4}\iff-(x+10)\ln4=W(-4^{-10}\ln4)\iff$$
$$x=-\frac{W(-4^{-10}\ln4)}{\ln4}-10.$$
And similarly for the third.