Find x: 312e^-0.14x=26e^0.2x

Question

anonymous · Answer

ugh. ???????????????????????????????????????????????????? idk

anonymous · Answer

im not much help

anonymous · Answer

i could help

ghostedly · Answer

Do you have any guesses of what x might be?

anonymous · Answer

idk, i didn't really work with natural logs for over a year

anonymous · Answer

give me a few and ill let you know what i think it is

mathmusician · Answer

Can you rewrite that using the equation thing

ghostedly · Answer

x = 0

ghostedly · Answer

First subtract the number from both sides...

anonymous · Answer

ye $$312e^{-0.14x}=26e ^{0.2}$$

ghostedly · Answer

I already told you the answer. It's 0.

anonymous · Answer

infinity

mathmusician · Answer

ln = 312

mathmusician · Answer

sorry ln312 = x

anonymous · Answer

er i don't think it's zero. the question asks for maximum total surplus :p

anonymous · Answer

infinity

mathmusician · Answer

ln312 = 26e^0.2

ghostedly · Answer

Does it need to be estimated?

mathmusician · Answer

$$26e ^{0.2} = 31.76 $$
$$\ln312 = 31.76$$

anonymous · Answer

@MathMusician sorry there's an x after 0.2, so that's not the answer. 

Anyways the actual question was "A camera company estimates that the demand fxn for its new digital camera is p(x)=312e^-0.14x and the supply function is estimated to be ps(x)=26e^0.2x, where x is measured in thousands. Compute the maximum total surplus"

So you have to get the equations equal and now I'm not sure where to go :p

mathmusician · Answer

oh okay i see what i did wrong

mathmusician · Answer

can you move the 312 to the other side