3x - 2^x - 1 = 0

Question

3x - 2^x - 1 = 0

Answer 1

We can always graph some points:

x | y

-1|-4.5

0 |-3

1 | 0

2 | 1

3 | 0

4 |-5

5 |-21

 

So to make our equation true, x = 1 or 3.

Answer 2

Separate the variable exponent from the rest of the equation by adding, then take the natural log of both sides. This will allow you to put the variable exponent in front of the natural log. Solve from there.