How to solve for x in this equation

e ^{-x} = 3e ^{-3x}

Question

How to solve for x in this equation

e ^{-x} = 3e ^{-3x}

anonymous · Answer

$$e ^{-x} = 3e ^{-3x}$$

inkyvoyd · Answer

Take the natural log of both sides.

anonymous · Answer

The original function is e ^{-x} = e ^{-3x}
and i did the first derivative and got the answer above

inkyvoyd · Answer

No, don't take the derivative.

anonymous · Answer

I got x= 0.55

but my book's answer is 0.38 or so

i dont know if i have differnciate wrong or what

anonymous · Answer

the question asks for extreme values, so need to find first derivative

inkyvoyd · Answer

Oh, Nevermind.

inkyvoyd · Answer

You took the derivative incorrectly

inkyvoyd · Answer

should be -e^(-x)=-3e^(-3x)

anonymous · Answer

yea, that's what i have too
and then set f'(x) to 0

anonymous · Answer

the 2 negative cancels out

inkyvoyd · Answer

Can you type out the exact question?

anonymous · Answer

Use algorithm for finding extreme values to determine the absolute maximum and minimum values of the function f(x) = $$e ^{-x} - x ^{-3x}$$

anonymous · Answer

sorry, that's e, not x

inkyvoyd · Answer

I'm getting a math processing error, leme swtich browsers.

anonymous · Answer

$$e ^{-x} - e ^{-3x}$$

anonymous · Answer

ok! thanks

inkyvoyd · Answer

y=e^(-x)-e^(-3x)
y'=-e^(-x)+3e^(-3x)
Since y'=0
e^(-x)=3e^(-3x)
I got 0.55 too (wolfram alpha input)
I think your textbook answer is wrong.

anonymous · Answer

ohhh i know why now
because that 0.38 is when u subsitute 0.55 in the f (x) function!

thanks for ur help!

inkyvoyd · Answer

0.o. I did absolutely nothing though.

anonymous · Answer

thankful for trying to help :)

inkyvoyd · Answer

oh :D