[Math] Problem to find the intersection of a exponential and linear function

Question

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*}

Answer 1

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