# Homework Help: Solve exponential equation

1. Nov 2, 2013

### surfy2455

*solved

Last edited: Nov 2, 2013
2. Nov 2, 2013

### Staff: Mentor

With equations like these, where the variable appears in the exponent and outside the exponent, there's not usually an easy way to solve the equations using algebra. I think your best bet is either to treat each side of the original equation as a function, and graph it, and then look for intersections of the two graphs.

For the first one, the powers of 2 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and so on. Since the left side is 200

3. Nov 2, 2013

### Staff: Mentor

I see that you started another thread here - https://www.physicsforums.com/showthread.php?t=720463. That gives some context to the problem. For one thing, n is an integer, as it represents the number of steps in an algorithm, or something related to that.

With that context, all you need to do is to find numbers n and n + 1 that straddle the exact solution. In other words, when you substitute that value of n in the equations, the left side is smaller than the right side. When you substitute n + 1, the left side is larger than the right side.

4. Nov 2, 2013

### surfy2455

Yes, I found the solutions by doing this method before I posted this, but the main intent was to see if there was a more discrete mathematical solution instead of the trial and error approach of plugging and validating.