I am really confused when working with logarithms. Can you help me understand how to calculate the ones in question 1, 3 and 5? Thank you.

 

 

WS4-LOGARITHMS NAME________________________________ 154
Sec # ___________ 1. Calculate the following. Whenever possible give the exact value. If an exact value can’t be given, round to 4
decimal places. If the value does not exist, state DNE. A. log 1.035 1 B. log 4 64 C. log 2 4 D. ln e E. log9 3 2. a) Change y log a x to log base 10. (Recall: the change of base formula) b) Change y log a x to log base e. (Recall: the change of base formula) 3. Consider S D 0.159 0.118log D . S is the slope of a beach and D is the average diameter
(in mm) of the sand particles on the beach. Suppose a particular beach rises 9 meters for every 100
meters inland. What size sand would you expect to find on that beach? 4. A. Sketch a graph of y 7 7 .
Consider and include the domain in your sketch.
log x B. Sketch a graph of y ln e x . 5. You and a friend plan to purchase cars in September. The initial value of your car will be $34,000
and will depreciate 17% each year. The initial value of your friend’s car will be $16,500 and will
depreciate 12% each year. You agree to exchange cars when their values are equal.
A. How long do you need to wait? (to the nearest month) What is the value of the cars? B. What would your depreciation rate have to be in order for the values of the cars to match at the
end of 7 years? (Assume your friend’s car depreciates 12% each year.) 6. It is predicted that the population of a particular state in 2005 will double by the year 2024
exponentially. Determine the annual, monthly and continuous growth rates. Write answers as a
percentage with 3 decimal places. Show all work.
a) annual growth rate: ________ b) monthly growth rate: ________ c) continuous growth rate:________

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