Assignment 11

1. Show how the rules for log(a*b) and log(aⁿ) come from rules for exponents.

2. Write (1/2)^t/350 in terms of the exponential function.

3. Assuming monthly compounding, how long does it take money invested at 5% to double? Repeat for continuous compounding.

4. We wish to fit the data below to a curve of the form N = A (1/s)^d. Take the log to get a linear equation for log(N) to fit, and then fit the data to this problem. Plot the original data, and the fitted curve.

N	s
28	¼
83	1/8
246	1/16
746	1/32

5. Solve the following for x.

a. ln(x²)=3

b. 2^x = 10^4-x

c. log_x(2)=1.5

6. pH is defined as –log₁₀(concentration of H⁺ ions in moles per liter). If a liquid has pH = 5.3, what is the H⁺ concentration?

7. If f(x) = 3^x, what is f^-1? Graph both on the same axes.