   # Exponents and Logarithms

Better Essays
Maryann Crisci
Mrs. Cappiello
Algebra 2/Trig, Period 6
1 April 2012
Exponents and Logarithms An exponent is the number representing the power a given number is raised to. Exponential functions are used to either express growth or decay. When a function is raised to a positive exponent, it will cause growth. However, when a function is raised to a negative exponent, it will cause decay. Logarithms work differently than exponents. Logarithms represent what power a base should be raised to in order to produce a specific given number. Logarithmic and exponential functions are often used together because they are inverse functions, and therefore “undo” one another. The natural exponential function and the natural logarithm are frequent examples. These functions have a base of the constant e, or Euler’s number. The natural exponential function is written as f(x)=ex. Its inverse, the natural logarithmic function, is written as f(x)=ln(x). The decay of radioactive substances can be represented by using an exponential function. The mass of the radioactive substance will decrease as time passes, but the rate of decay and the mass of the substance will always remain directly proportional. The decay of radioactive substances can be expressed by the function m(t)=m0e-rt, where m(t) represents the mass remaining at time t, r represents the rate of decay, and m0 represents the initial mass. When the rate of decay is expressed by half-life, the rate of decay expressed as a proportion of the mass can be found by substituting the half-life into the equation ½=1∙e-rh. This is because when h, or the half-life, is equal to t, or time, then the mass of 1 unit becomes ½ unit. An example of a radioactive substance that will decay over time is Polonium-210. Polonium-210 has a half life of 140 days. This half-life was plugged into the equation ½=1∙e-rh in order to find the rate of decay expressed as a proportion of the mass, or r. 140 was plugged in for h. In order to solve the

Cited: "Chemical Elements.com - Sodium (Na)." Chemical Elements.com - An Interactive Periodic Table of the Elements. N.p., n.d. Web. 4 Apr. 2012. . "Graphing Calculator." Holt McDougal Online. N.p., n.d. Web. 4 Apr. 2012. . "sodium (Na) (chemical element) :: Nuclear properties -- Britannica Online Encyclopedia." Encyclopedia - Britannica Online Encyclopedia. N.p., n.d. Web. 4 Apr. 2012. .

## You May Also Find These Documents Helpful

• Good Essays

History of Logarithms Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. Napier's logarithms were published in 1614; Burgi's logarithms were published in 1620. The objective of both men was to simplify mathematical calculations. This approach originally arose out of a desire to simplify multiplication and division to the level of addition and subtraction. Of course, in this era of the cheap hand calculator, this is not necessary anymore but it still serves…

• 621 Words
• 3 Pages
Good Essays
• Good Essays

HISTORY OF LOGARITHMS 1ST SOURCE: (sosmath.com) Logarithms were invented independently by John Napier, a Scotsman, and by Joost Burgi, a Swiss. The logarithms which they invented differed from each other and from the common and natural logarithms now in use. Napier's logarithms were published in 1614; Burgi's logarithms were published in 1620. The objective of both men was to simplify mathematical calculations. Napier's approach was algebraic and Burgi's approach was geometric. Neither…

• 567 Words
• 3 Pages
Good Essays
• Good Essays

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10 × 10 × 10 = 103. More generally, if x = by, then y is the logarithm of x to base b, and is written y = logb(x), so log10(1000) = 3. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by navigators, scientists…

• 394 Words
• 2 Pages
Good Essays
• Satisfactory Essays

PRINCE ALFRED COLLEGE YEAR 10 ADVANCED MATHEMATICS TEST 4: Part 2 Thursday 12-08-09 TOPIC: Indices (Exponents) & Logarithms & modelling Name: Pastoral Care Group: 10 Maximum mark Your mark Grade % mark Class average % 60 Graphics…

• 355 Words
• 2 Pages
Satisfactory Essays
• Satisfactory Essays

Number Expanded form Exponential form Base and exponent 10000 10 × 10 × 10 × 10 104 base 10, exponent 4 base , exponent 5 64 2 × 2 × 2 × 2 × 2 × 2 26 base 2, exponent 6 64 (–2) × (–2) × (–2) × (–2) × (–2) × (–2) (–2)6 base –2, exponent 6 –32 (–2) × (–2) × (–2) × (–2) × (–2) (–2)5 base –2, exponent 5 Example 1: Write the following in exponential form. a. Minus nine to the power of six b. One fourth to the power of five c. Three square to the power of five Solution:…

• 264 Words
• 2 Pages
Satisfactory Essays
• Satisfactory Essays

Laws of Exponents Here are the Laws (explanations follow): Law | Example | x1 = x | 61 = 6 | x0 = 1 | 70 = 1 | x-1 = 1/x | 4-1 = 1/4 | | | xmxn = xm+n | x2x3 = x2+3 = x5 | xm/xn = xm-n | x6/x2 = x6-2 = x4 | (xm)n = xmn | (x2)3 = x2×3 = x6 | (xy)n = xnyn | (xy)3 = x3y3 | (x/y)n = xn/yn | (x/y)2 = x2 / y2 | x-n = 1/xn | x-3 = 1/x3 | And the law about Fractional Exponents: | | | Laws Explained The first three laws above (x1 = x, x0 = 1 and x-1 = 1/x) are just part of…

• 569 Words
• 3 Pages
Satisfactory Essays
• Satisfactory Essays

the following: 4. 5. Convert to log form 6. Evaluate the logarithm without a calculator: 7. Solve the following equations: 8. Fill in the chart and graph: x 1/4 1/2 0 2 4 8 16 9. A biologist is researching a newly-discovered species of bacteria…

• 438 Words
• 6 Pages
Satisfactory Essays
• Good Essays

and table lookups. However logarithms are more straightforward and require less work. It can be shown using complex numbers that this is basically the same technique. From Napier to Euler John Napier (1550–1617), the inventor of logarithms. The method of logarithms was publicly propounded by John Napier in 1614, in a book titled Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Rule of Logarithms). Joost Bürgi independently invented logarithms but published six years after…

• 1118 Words
• 5 Pages
Good Essays
• Good Essays

The Laws of exponents Study Guide…page 1 of 3 Base Number: The number that multiplies by itself as many times as the exponent tells it to. Exponent: The small number that tells the base number how many times to multiply by itself. NOTE: numbers and variables without exponents actually have an invisible 1 as their exponent. | | | |Multiplying exponents…

• 652 Words
• 3 Pages
Good Essays
• Good Essays

Earthquakes and Logarithms Earthquakes are responsible for a wast majority of natural hazards on our planet. This natural geological phenomena are almost impossible to predict, and they occur usually in zones of the planet that are prone to movement in the uppermost crust of the earth. Certain areas are more likely to experience earthquakes, and also the aftermath of the earthquakes can be just as destructive or sometimes even more. Different methods of measuring earthquakes have been implemented…

• 1027 Words
• 5 Pages
Good Essays