Question 126824
Solve for x:
{{{-5*e^(-x) + 9 = 6}}} Subtract 9 from both sides.
{{{-5*e^(-x) = -3}}} Divide both sides by -5.
{{{e^(-x) = 3/5}}} 
{{{1/e^x = 3/5}}} Invert both sides.
{{{e^x = 5/3}}} Now take the natural log of both sides.
{{{ln(e)^x = ln(5/3)}}}
{{{x*ln(e) = ln(5/3)}}} But {{{ln(e) = 1}}}, so...
{{{x = 0.512}}}
Check:
{{{-5*e^(-x) + 9 = 6}}} Substitute x = 0.512
{{{-5*e^(-0.512) + 9 = 6}}}
{{{-5*0.6+9 = 6}}}
{{{-3+9 = 6}}}
{{{6 = 6}}}