solve 4^xe^(7x+5) = 21

ln((4^x)e^(7x+5)) = ln21; apply a natural log on both sides of the equation as an exponential containing e is involved 

ln4^x + ln(e^(7x+5)) = ln21; using logarithm rules you can seperate the single log on the LHS to form to logs as ln(ab) = lna + lnb

xln4 + 7x + 5 = ln21; using logarithm rules we can move down the power on the ln4e^x and lne^(7x+5) and since lne is 1 we are left with xln4+7x+5

x(ln4 + 7) = ln21 - 5; factor out the variable components and move all numbers with no variable to the same side of the equation

x = (ln21-5)/(ln4+7); divide through by the coefficient of x