Question 71077
1) Solve for x:
{{{(e^x)(e^(3x)) = 4}}} Take the natural log of both sides.
{{{ln((e^x)(e^(3x))) = ln(4)}}} Apply the product rule for logarithms to the left side.
{{{ln(e^x) + ln(e^(3x)) = ln(4)}}} But {{{ln(e^x) = x}}}
{{{x + 3x = ln(4)}}} Simplify.
{{{4x = ln(4)}}} Divide both sides by 4.
{{{x = (1/4)ln(4)}}} Evaluate using your calculator or log tables.
{{{x = 0.3466}}} Approximately.

2) Solve for x:
{{{e^9 = ((e^x)^3)(1/e^9)}}} Multiply both sides by {{{e^9}}}
{{{(e^9)(e^9) = (e^x)^3}}} Simplify both sides.
{{{e^18 = e^(3x)}}} Take the natural log of both sides.
{{{ln(e^18) = ln(e^(3x))}}}
{{{18 = 3x}}} Divide both sides by 3.
{{{x = 6}}}