# Problem to find the intersection of a exponential and linear function

I have the problem to find the intersection of a exponential and linear function.
My math teacher can't help me, but I'm interested how I can solve this. I tried to use the equating method, but it doesn't worked.
Do I have to use the Newton's method or should I change the variables to simplify the problem?

Here is the code:

\begin{eqnarray*}f_1(x)&=&700*x+1200\\f_2(x)&=&3^x\\f_1&=&f_2\\700*x+1200&=&3^x | / 3\\\frac{ln[700*x+1200]}{3}\ &=&ln(x)\end{eqnarray*}

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## migrated from mathoverflow.netJul 3 '13 at 14:58

This question came from our site for professional mathematicians.

It can't be solved explicitly; you'll have to use numerical methods. You might be able to express the solution in terms of the Lambert W function. – David Mitra Jul 3 '13 at 15:05
Depending on how much precision you want and how patient you are, bisection is a fairly no-brains way to get an approximation even if all you have is paper and pen(cil). – Jason Knapp Jul 3 '13 at 15:07
Your last line seems wrong. – WillO Jul 3 '13 at 15:33
Your last line should have $x \ln 3$. As usual, when the question involves an exponential, the answer involves the good old Lambert the fearless lion's W-function. – marty cohen Jul 3 '13 at 15:36
yep sorry, I haven't assigned the last line. Thank you for all comment answers! – sinaneker Jul 3 '13 at 15:41

## 1 Answer

Unfortunately, this sort of problem requires the use of some numerical method (such as Newton's method, which you mention) to solve.

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