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)
|
|
|
