Math
posted by D.S. .
10e^(3x7)= 5
So what I've done is rewritten it as:
(3x7)ln10e = ln5
Now I'm a little lost as to what to do next...

Find the value of in10 and in5
multiply the value of in10 wit the varables in the brackets
collect the like terms i.e live the varable with the x term on the left hand side and the others on the right
then solve for x from there.
Goodluck 
Your start was incorrect...
the exponent does not apply to the 10, only to the base of e
so ...
e^(3x7) = 5/10= .5
now take ln of both sides
(3x7) ln e = ln .5 , but ln e = 1
3x7 = ln .5
3x = 7 + ln .5
x = (7 + ln .5)/3 , and it is buttonpushing time