[RESOLVED] Exponential question

[Yunie]

Solve e^(x-1) = 9 - 18e^(1-x)

I have no idea on how to do this...Please help.

[krtxmrtz]

Solve e^(x-1) = 9 - 18e^(1-x)

I have no idea on how to do this...Please help.

Hint 1:
e^{(1 - x)} = 1 / e^{(x - 1)}

Hint 2:
Call e.g. y = e^{(x - 1)}, work all the way with y and once you've found the answer for y calculate x.

[Yunie]

e^(x-1) = 9 - 18e^(1-x)

= e^(x-1) = 9 - 18/e^(x-1)

= e^(x-1) = [9e^(x -1) - 18] / e ^9x-1)

......

Is the above steps correct?

Then, how to continue? I kind of feel that the above steps are somehow weird...Please correct me, thanks.

[krtxmrtz]

e^(x-1) = 9 - 18e^(1-x)

= e^(x-1) = 9 - 18/e^(x-1)

= e^(x-1) = [9e^(x -1) - 18] / e ^9x-1)

......

Is the above steps correct?

Then, how to continue? I kind of feel that the above steps are somehow weird...Please correct me, thanks.

So, you've ignored my second hint and now you're in trouble... Well, if you do as I suggested:

y = e^{x - 1}

then your equation becomes

y = 9 - 18 / y
y² = 9y - 18
y² - 9y + 18 = 0

which does certainly look much easier, does it not? Hopefully you know how to pick up from here, solve for y and then invert the above transformation to finally come out with x.

[Yunie]

I see I see...Thank you so much krtxmrtz! And, yup, I know how to continue from the above steps...Thank you!