SOLUTION: Solve the equation for x. e^(ax) = Ce^(bx), where a is not equal to b

Question 208905: Solve the equation for x.
e^(ax) = Ce^(bx), where a is not equal to b
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Solve the equation for x.
e^(ax) = Ce^(bx), where a is not equal to b
.
Applying "log rules":
e^(ax) = Ce^(bx)
Divide both sides by e^(bx):
e^(ax)/e^(bx) = C
Rewriting the left side:
e^(ax-bx) = C
Take the ln of both sides:
ax-bx = ln(C)
Factor the left:
x(a-b) = ln(C)
Dividing we get:
x = ln(C)/(a-b)

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