Is there a general way to solve equations involving both a multiple of x and a power of x?

Say I’m trying to solve 2^x – 10 = 20 for x. I want to do it using algebra. Is this possible? If not, can I use calculus somehow? I’m looking for a way to solve it other than qualitatively (i.e., looking at a graph).

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This problem arose when I was trying to find the point at which two graphs intersect. They were f(x) = 2^(x-1)/100 + 0.005 and g(x) = 5x + 10. The problem is for a middle school lesson I’m teaching. Finding their intersection algebraically was something I wanted to do with them since they’re an advanced class, but now I realize even I can’t do it. The problem is about a kid who earns $10 a day, plus $5 for every chore he does. On the first day of the month, he does one chore, on the 2nd, he does 2, and so on. He hates doing dishes, so his friend offers to do the dishes for him for a “bargain” price. He charges 1 cent on the first day, and doubles the price each day (2 cents on the 2nd, 4 cents on the 3rd, 8 cents on the 4th, etc). The problem is supposed to teach them about the difference between exponential and linear functions, and that’s where the graphs come from.