Solve for $x$ (both 2 values as plotted on graph):

Question

find a way to solve for x: $$ 2^x = x + 5$$

You can easily see one of the values is $3$. If you plot this in a graph, with $y=2^x$ and $y=x+5$, you'll see it has 2 values. If, in a calculator like casio fx-991E series, PLUS perhaps, you plunk in $2^x=x+5$ and hit solve (shift + calc), you'll get the other value, as the calculator solves from left to right.

But the thing is to find a manual, universal way to solve it

Answer 1

observe that for $2^x\gt x+5$ for$x\ge 4$

which follows by induction

again $2^x\lt x+5$ for $x\lt 2$

which again follows by induction

so $2\lt x\lt 4$

i think it would be helpful!!!