How to solve this equation?

50000x = 2^x

You can't solve this kind of equation algebraically. Use a numerical method (for instance Newton's method) to get an approximate result:

2^x-50000x = 0

Using Newton's method:

x_{n+1} = x_n - (2^x_n-50000x_n)/(ln(2) * 2^x_n - 50000)

Start with x_1 = 0 or x_1 = 19 to get the two possible values for x.
 
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