Solve the equation for x.
e^ax=Ce^bx, where a cannot equal b
Can someone explain this pleaseee!
take the ln of each side...
ax=ln C + bx
x(a-b)= ln C solve for x.
im confused...to many letters
To solve the equation e^ax = Ce^bx, where a and b are constants and a cannot equal b, we can use logarithms.
First, divide both sides of the equation by Ce^bx:
e^ax / Ce^bx = 1
Next, we can use the properties of logarithms to simplify further. Take the logarithm (base e) of both sides of the equation:
ln(e^ax / Ce^bx) = ln(1)
Using the logarithm properties, this simplifies to:
ln(e^ax) - ln(Ce^bx) = 0
Applying the logarithm property that ln(a/b) = ln(a) - ln(b), this becomes:
ax - bx - ln(C) = 0
Now, we can rearrange the equation:
x(a - b) = ln(C)
Finally, solving for x, we can divide both sides by (a - b):
x = ln(C) / (a - b)
So the solution for x is x = ln(C) / (a - b).