Question 1147557
<br>
Let {{{u = e^(sqrt(x))}}}<br>
Then the equation is<br>
{{{2u^2 = 7u-3}}}
{{{2u^2-7u+3 = 0}}}
{{{(2u-1)(u-3) = 0}}}<br>
{{{u = 1/2}}}  or  {{{u = 3}}}<br>
(1) {{{e^(sqrt(x)) = 1/2}}}
{{{e^x = 1/4}}}
{{{x = ln(1/4)}}}<br>
(2) {{{e^(sqrt(x)) = 3}}}
{{{e^x = 9}}}
{{{x = ln(9)}}}<br>