Question 79204
Solve for x
10^(2x-1)= e^(4x-3)
{{{ln(10^(2x-1))=ln(e^(4x-3))}}}  
you can either take the common log, or the natural log of both sides.  I chose natural log so that I didn't have to deal with e as a number.
{{{(2x-1)ln(10)=(4x-3)ln(e)}}}  ln(e)=1
{{{(2x-1)ln(10)=4x-3}}}  distribute ln(10)
{{{2xln(10)-ln(10)=4x-3}}}  Get x's to one side of = sign.
{{{2xln(10)-4x-ln(10)=4x-4x-3}}} get things without x's to the other side.
{{{2xln(10)-4x-ln(10)+ln(10)=ln(10)-3}}}
{{{2xln(10)-4x=ln(10)-3}}} factor out the x's
{{{x(2ln(10)-4)=ln(10)-3}}} divide by the coefficient of x
{{{x(2ln(10)-4)/(2ln(10)-4)=(ln(10)-3)/(2ln(10)-4)}}}
{{{x=(ln(10)-3)/(2ln(10)-4)}}}  Put it in your calculator.
{{{x=-1.15243}}}
Happy Calculating!!!!