Question 865079
{{{4^x=2(3^x)}}} Start with the given equation.



{{{ln(4^x)=ln(2(3^x))}}} Apply the natural log to both sides



{{{ln(4^x)=ln(2)+ln(3^x)}}} Using <a href="http://www.purplemath.com/modules/logrules.htm">rule 1</a>



{{{x*ln(4)=ln(2)+x*ln(3)}}} Using <a href="http://www.purplemath.com/modules/logrules.htm">rule 3</a>



{{{x*ln(4)-x*ln(3)=ln(2)}}} Subtract {{{x*ln(3)}}} from both sides.



{{{x(ln(4)-ln(3))=ln(2)}}} Factor out x



{{{x*ln(4/3)=ln(2)}}} Using <a href="http://www.purplemath.com/modules/logrules.htm">rule 2</a>



{{{x=ln(2)/ln(4/3)}}} Divide both sides by {{{ln(4/3)}}} to isolate x.



{{{x=2.40942083965}}} Using a <a href="https://www.google.com/search?q=ln(2)/ln(4/3)">calculator</a> here



{{{x=2.41}}} Rounding to 3 significant figures