Question 542546
Solve for x:
{{{2.0e^(-1.5x) = 1}}} First, divide both sides by 2.
{{{e^(-1.5x) = 1/2}}} Substitute {{{1/2 = 0.5}}}
{{{e^(-1.5x) = 0.5}}} Now take the natural logarithm of both sides.
{{{ln(e^(-1.5x)) = ln(0.5)}}} Apply the "power rule" to the left side.
{{{-1.5xln(e) = ln(0.5)}}} Substitute {{{ln(e) = 1}}}
{{{-1.5x = ln(0.5)}}} Divide both sides by -1.5
{{{x = ln(0.5)/-1.5}}}  Evaluate.
{{{x = 0.4621}}} Approx.