Without using a calculator, explain why the solution to each equation must be a real number between 1 and 2.
21^x = 30

Explanation:

  21^1 = 21 < 30

  21^2 = 21² = 441 > 30

30 lies between 21^1 and 21^2.

21^x is a continuous function, so the value of x that makes 21^x = 30 must lie between 1 and 2, according to the intermediate value theorem.

_____

Using a calculator, we find x ≈ 1.117153.

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.