Question 81497
This is a classic problem of "undo-ing" the operations of math in order to solve for x.


2+6e(4x)=19 


First, you need to "undo" the 2 that is added to the term that contains the x.  Of course, you do this by subtracting 2 from each side of the equation:


{{{6e^(4x) = 17}}}


Next, you must "undo" the 6 that is multiplied times the term containing the x:
{{{e^(4x) = 17/6}}}


Next, you must "undo" the "e" raised to the power.  The inverse of "e" raised to the power is the "ln" function, so you must take the "ln" of each side:
{{{ln(e^(4x)) = ln(17/6)}}}
{{{4x=ln(17/6)}}}


Finally, undo multiplication of the x times 4 by either dividing both sides by 4 or by multiplying both sides times {{{1/4}}}.


Final answer {{{x= (ln(17/6))/4 }}}
{{{x= .2604}}}


R^2 at SCC