Question 152229
It's not clear how this problem is to be read!
1) {{{e^x+e^x + 1 = 250}}} or
2) {{{e^x+e(x+1) = 250}}} I suspect that this is what you wanted, so let's go with it.

{{{e^x+e^(x+1) = 250}}} Substitute {{{e^(x+1) = e^x * e^1}}}
{{{e^x+e^x*e = 250}}} Factor out {{{e^x}}}.
{{{e^(x)(1+e) = 250}}} Divide both sides by {{{(1+e)}}}
{{{e^x = 250/(1+e)}}} Take the natural log of both sides.
{{{ln(e^x) = ln(250/(1+e))}}} Substitute: {{{ln(e^x) = x}}}
{{{x = ln(250/(1+e))}}}
{{{x = ln(250/3.72)}}}
{{{x = ln(67.235355)}}} 
{{{x = 4.21}}} Approximately.