Exponential and Logarithmic Functions 2.2 Logarithmic Functions MATH14 • Logarithmic Function with base b • Graph of Logarithmic Function • Natural Logarithmic Function • Properties of Logarithmic Functions • Exponential and Logarithmic Equations Logarithmic Function with base b Definition: The logarithmic function with base b is the inverse of the exponential function with base b. y logb x Note: Dom f if and only if x b y Rng f Logarithmic Function
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Gerald Hopkins‚ E.E. Cummings‚ and Emily Dickinson all displayed the beauty of spring in multiple different ways. Hopkins used his poem “Spring” by displaying the rebirth of the environment. Cummings’ poem “in Just” shows the power of the God of nature. Dickinson’s poem “I taste a liquor never brewed” acknowledges her love of spring by comparing it to be intoxicating. The spring has many beautiful transitions. All throughout Hopkins’ poem he exhibited imagery. In the spring all the greenery returns
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it was widely praised by both blacks and whites‚ although it was not long before critics of Washington’s position emerged to challenge his leadership. Early complaints about Washington’s accommodation to the white South came from the black scholar W. E. B. Du Bois and others. But until he died in 1915‚ Washington was the most influential black leader in America‚ and the most famous black celebrity in the country‚ an adviser to presidents and representative to European heads of state. His autobiography
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Electronic Business E-business (electronic business)‚ derived from such terms as "e-mail" and "e-commerce‚" is the conduct of business on the Internet‚ not only buying and selling but also servicing customers and collaborating with business partners. One of the first to use the term was IBM‚ when‚ in October‚ 1997‚ it launched a thematic campaign built around the term. Today‚ major corporations are rethinking their businesses in terms of the Internet and its new culture and capabilities. Companies
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EXPONENTIAL AND LOGARITHMIC FUNCTIONS I.EXPONENTIAL FUNCTION A. Definition An exponential function is a function defined by f(x) = ax ‚ where a > 0 and a ≠ 1. The domain of the function is the set of real numbers and the range is the set of positive numbers. B. Evaluating Exponential Functions 1. Given: f(x) = 2x‚ find a. f(3) = ____ b. f(5) = _____ c. f(-2) = ______ d. f(-4) = ______ 2. Evaluate f(x) = ( 1)x if 2 a. x = 2 ____ b. x = 4 _____ c. x = -3 ______ d
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W.E.B Du Bois Student’s Name Institutional Affiliation W.E.B Du Bois America at the decades between XIX-XX centuries made its first efforts on the establishment of the democratic and force country. Civil war in the USA between the industrial North and the agrarian slaveholding South became 1861-1865 a turning point in the American history. The period of a post-war emptiness and fatigue came to change the innocent optimism of the young democratic nation
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In the early 1900’s both Booker T. Washington and W.E.B Du Bois presented a plan for racial justice. While the two plans fought for the same people‚ their approach‚ ideologies‚ and goals differed. Both men were brave to speak out‚ but overall Du Bois created a plan that was radical and one that represented the African American community well. Du Bois most compelling tool used in his plan for racial justice lies in his word choices. The way he uses metaphors like “the veil” and “double consciousness”
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William Edward Burghardt famously recognized as W.E.B Dubois was born on February 23‚ 1868 in Great Barrington‚ Massachusetts. W.E.B Dubois was famously recognized as an American sociologist‚ historian‚ civil rights activist‚ Pan-Africanist‚ author and editor. W.E.B Dubois was born to parents Alfred Dubois and Mary Silvina Du Bois who was apart of a diminutive group of released blacks. During Dubois’ early childhood‚ his parents got divorced in 1870 when W.E.B was two years of age and he lived with
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Taipei European SchoolMath Portfolio | VINCENT CHEN | Gold Medal Heights Aim: To consider the winning height for the men’s high jump in the Olympic games Years | 1932 | 1936 | 1948 | 1952 | 1956 | 1960 | 1964 | 1968 | 1972 | 1976 | 1980 | Height (cm) | 197 | 203 | 198 | 204 | 212 | 216 | 218 | 224 | 223 | 225 | 236 | Height (cm) Height (cm) As shown from the table above‚ showing the height achieved by the gold medalists at various Olympic games‚ the Olympic games were not held in
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LOG INVESTIGATION 1. INTRODUCTION The following assessment aims to investigate logarithms and several different expressions. The following sequences (from now on referred to as P roblem1 ) is in the form of an = logmn mk ‚ where n represents the term number and an represents the given answer. 1. a1 = log2 8‚ a2 = log4 8‚ a3 = log8 8‚ a4 = log16 8‚ a5 = log32 8‚ ... 2. a1 = log3 81‚ a2 = log9 81‚ a3 = log27 81‚ a4 = log81 81‚ ... 3. a1 = log5 25‚ a2 = log25 25‚ a3 = log125 25‚ a4 = log625
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