How do you get a linear equation to equal exponential?

Question

i was working on a math problem and figured out I don't know how to make a linear and exponential equation set equal. for example,

2x+1=2^x.

How would you solve a problem like this

Answer 1

Use numerical analysis.

1.  Graph the eqns and read off the graph.

2.  Babylonian method.

3.  Newton's method.

4.  Punch the eqns into Excel and zoom in to see when they're approxiamately equal.

Answer 2

I'm not sure how to solve it algebraically but, could you perhaps graph each function separately to determine where the two functions meet?

For the left side, the equation y = 2x + 1 defines a line with a slope of 2 and a y-intercept of 1. Going positive from the y-axis, from point (0, 1), it next passes through points (1, 3), (2, 5), (3, 7), etc in a straight line.

For the right side, the equation y = 2^x defines an exponential function. Going positive from the y-axis, from point (0, 1), it next passes through points (1, 2), (2, 4), (3, 8), etc.

Between x = 2 and x = 3, the two functions cross.

In addition to the point (0, 1), that point is the other value of x which satisfies the equation.