Solve the eqation for x.....?

Question

e^(ax) = Ce^(bx)

(Where a does not equal b)

Answer 1

Take the natural log of both side

ln (e^(ax)) = ln (Ce^(bx))

ln(e^(ax)) = ln(C) + ln(e^(bx))        [ ln(ab) = ln(a) + ln(b)]

ax = ln(C) + bx                                 [ln (e^x) = x]

ax = C + bx                                 [C is a constant so ln(C) is  also a constant denoted by C]

ax - bx = C

x(a-b) = C

x = C / (a-b)

Hope that helps!

Answer 2

ln(e^(ax))=ln(Ce^(bx))

ax=lnC+ln(e^(bx))

ax=lnc+bx

ax-bx=lnC

x(a-b)=lnC

x=(lnC)/(a-b)