e^x + x = 5

How do you solve this and what is the answer? It is a review question for a math quiz and I have tried many times to solve this. It will probably require natural logs because that is what I am doing currently.

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- 04-21-2002golfinguy4Math Help
e^x + x = 5

How do you solve this and what is the answer? It is a review question for a math quiz and I have tried many times to solve this. It will probably require natural logs because that is what I am doing currently. - 04-21-2002UnregisteredRe: Math HelpQuote:

*Originally posted by golfinguy4*

**e^x + x = 5**

How do you solve this and what is the answer? It is a review question for a math quiz and I have tried many times to solve this. It will probably require natural logs because that is what I am doing currently.

e^x = 5 - x

ln(e^x) = ln(5 - x)

thus, x = ln(5 - x).

i don't know if that's right though... - 04-21-2002Unregistered
i forgot to mention that ln e^x = x.

- 04-21-2002Unregistered
or was it e^(ln x) = x?

- 04-21-2002SilentStrike
e^(ln(x)) = ln(e^(x)) = x

e^x != x - 04-21-2002golfinguy4
I have gotten that far. However, x=ln(5-x) doesn't solve for x because there are x's on both sides of the equation.

P.S. It is both - 04-21-2002ygfperson
1.30656

i got the value by writing a program to find values that fit the equation. i'm just as baffled as y'all are, but hopefully this will help - 04-21-2002Procyon
I don't think that equation can be solved non-numerically. I have Mathematica, and it gave the answer as

x = 5 - ProductLog[e^5]

which doesn't say much more than the original equation. It numerically evaluates to

1.3065586410395

which is about as good an answer as you're going to get.

If this is for a high school algebra class, I think your teacher goofed. - 04-21-2002golfinguy4
yfg, I can get that answer graphically by finding the intersection on my calc but I want to be able to find it algebraically b/c that is the way my teacher wants us to solve it.

Procyon: What the heck is productlog?

P.S. It is for a Pre-Calc class and from the book. - 04-21-2002ygfperson
i'm in pre-calc too, and i've never seen that kind of thing before. i think the book made a mistake or something

- 04-21-2002ProcyonQuote:

*Originally posted by golfinguy4*

Procyon: What the heck is productlog?

ProductLog[z] satisfies the differential equation dw/dz = w/(z(1+w)).

It's approximately equal to x - x^2 + 3/2 x^3 - 8/3 x^4.

There's apparently no way to solve this algebraically. I think your book is probably in error. - 04-22-2002golfinguy4
I saw my teacher today. She told me that it couldn't be done algebraically and the book was only wanting me to do it graphically. I assumed that any problem could be solved more than 1 way, guess I was wrong.