Reminder Round all answers to two decimal places unless otherwise indicated.
Using the Laws of Logarithms For Exercises 1 through 6, suppose that
To evaluate:
The given expression.
Answer to Problem 1E
Solution:
The expression
Explanation of Solution
Given:
The values
The expression is
Approach:
Following laws of logarithms are to be referred wherever applicable:
1) Product law:
2) Quotient law:
3) Power law:
Calculation:
Consider the expression.
Substitute
Therefore, the expression
Conclusion:
Hence, the expression
Want to see more full solutions like this?
Chapter 4 Solutions
FUNCTIONS AND CHANGE COMBO
- Rounding to three decimal places, approximate log342.arrow_forwardBody Surface Area There is a mathematical relationship between an infants weight and total body surface area BSA, given by Aw=4.688w0.8168-0.0154log10w, Where w is the weight in grams and Aw is the BSA in square centimetres. Source: British Journal of Cancer. a. Find the BSA for an infant who weights 4000 g. b. Find A'4000 and interpret your answer. c. Use a graphing calculator to graph Aw on 2000,10,000 by 0,6000.arrow_forwardRichter Scale The Richter scale provides a measure of the magnitude of an earthquake. In fact, the largest Richter number M ever recorded for an earthquake was 8.9 from the 1933 earthquake in Japan. The following formula shows a relationship between the amount of energy released and the Richter number. M=23logE0.007, Where E is measured in kilowatt-hours. Source: Mathematics Teacher. a. For the 1933 earthquake in Japan, what value of E gives a Richter number M=8.9?. b. If the average household uses 247 kWh per month, how many months would the energy released by an earthquake of this magnitude power 10 million household? c. Find the rate of change of the Richter number M with respect to energy when E=70,000 kWh. d. What happens to dM/dE as E increases?arrow_forward
- Convert to logarithmic form: (a) 32=9 (b) 712=7 (c) (13)x=127arrow_forwardUse a calculator to help solve each problem. Bluegill population A Wisconsin lake is stocked with 10,000 bluegill. The population is expected to grow exponentially according to the model Pt=P02t/2. How many bluegill will be in the lake in 5 years?arrow_forwardBuffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo bison herd that spends falls and winters in the park. The herd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the logistic formula N=3151+14e0.23t Here t is the number of years since the beginning of 2002, the first year the herd is unmanaged. a. Make a graph of N versus t covering the next 30 years of the herds existance corresponding to dates up to 2032. b. How many buffalo are in the herd at the beginning of 2002? c. When will the number of buffalo first exceed 300?. d. How many buffalo will there eventually be in the herd? e. When is the graph of N, as a function of t, concave up? When is it concave down? What does this mean in terms of the growth of the buffalo herd?.arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningFunctions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning