Question 534035
Solve for x:
{{{e^0.5x = 3^(1-2x)}}} Take the natural log of both sides.
{{{Ln(e^(0.5x)) = Ln(3^(1-2x))}}} Apply the "power rule" for logarithms.
{{{0.5xLn(e) = (1-2x)Ln(3)}}} Substitute {{{Ln(e) = 1}}} and {{{Ln(3) = 1.1}}}approx.
{{{0.5x = (1-2x)(1.1)}}} Evaluate.
{{{0.5x = 1.1-2.2x}}} Add 2.2x to both sides.
{{{2.7x = 1.1}}} Divide both sides by 2.7
{{{x = 1.1/2.7}}}
{{{x = 11/27}}}
{{{x = 0.407}}}approx.