# Northern Star Online Properties of Logarithms and Solving Exponential Equations Problems – Assignment Help

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Part 6-4: e and Natural Logarithms

2. Suppose \$4449 is invested at 11% compounded continuously for 7 years. What is the annual yield percent to the nearest hundredth?

3. Suppose \$4449 is invested at 11% compounded continuously for 7 years. How much money will be worth after that time?

6. The population of New Zealand in 1990 was about 3,376,000 with an average growth rate of 2.7%. If this growth rate continues, use the Continuous Change Model to predict New Zealand’s population in 2008.

7. A satellite has a radioisotope power supply, with power output given by

P = 73e-t/347

Where t is the time in days and P is the power output in watts.
What is the power output to nearest hundredth of a watt at the end of its first year?

8. A satellite has a radioisotope power supply, with power output given by

P = 73e-t/347

Where t is the time in days and P is the power output in watts.
When the power output drops below 8 watts, there will be insufficient power to operate the satellite. How many days will the satellite be operational?

10. Explain HOW you would find the answer to ln e7.1

Part 6-5: Properties of Logarithms

Use the fact that loga 4 = .782 and loga 3 = .654 and the property of logarithms to answer the following for Questions 1- 4.

1. Evaluate loga 3/4 =

2. Evaluate loga 48 =

3. Evaluate loga 27 =

4. Evaluate loga 3a4 =

5. Find an expression for A that does not involve logarithms

ln A = 2 ln B – 4 ln C

6. Write a linear function for log y which is equivalent to y = 400(1.08)x

7. Write a exponential equation in the form A = c*d^t equivalent to ln A = 1.7t + 8.2

Part 6-6: Solving Exponential Equations

5. If you invest money at 12.3% compounded continuously. How many years, to nearest tenth, will it take to double?

6. Which expression(s) could be entered into your calculator to produce a graph of y = log7 x

Select one or more:

a. y = log 7/log x

b. y = log x/log 7

c. y = ln 7/ln x

d. y = x/7

e. y = ln x/ln 7

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