Question 71077
{{{e^x * e^(3x) = 4}}}Start with given expression
{{{e^(x+3x) = 4}}}The left side can be written as {{{e^(x+3x)}}} since {{{e^x*e^y=e^(x+y)}}}
{{{ln(e^(x+3x)) =ln 4}}}Take natural log of both sides, this undoes the natural base e
{{{4x=ln 4}}}Solve for x by dividing both sides by 4
{{{x=(ln 4)/4=0.34657359}}}Approximately
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Do the same thing to the next problem
{{{e^9 = (e^x)^3 (1/e^9)}}}Start with given expression
{{{e^9 = e^(3*x)/e^9}}}The right side can be rewritten as {{{e^(3x)}}} since {{{e^x^y=e^(x*y)}}} (in other words {{{e^x^3=e^(3x)}}})
{{{e^18 = e^(3*x)}}}Multiply both side by e^9
{{{ln(e^18) =ln (e^(3*x))}}}Take natural log of both sides, this undoes the natural base e
{{{18 = 3*x}}}Solve for x by dividing both sides by 3
{{{x=18/3=6}}}