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The expression 25 is just a shorthand way of writing ‘multiply 2 by itself 5 times’. The number 2 is called the base, and 5 the exponent. Similarly, if b is any real number then b3 stands for b b b. Here b is the base, and 3. × ×. the exponent. If n is a whole number, bn stands for b b b . × × · · · ×. n factors.
- Exponentials and Logarithms - The University of Sydney
The Relationship between Exponentials and Logarithms To...
- Exponentials and logarithms: applications and calculus
In this booklet we will demonstrate how logarithmic...
- Exponentials and Logarithms - The University of Sydney
Exponentials and Logarithms. 1 Exponentials. We have already met exponential functions in the notes on Functions and Graphs.. EF. A function of the form f ( x ) = ax , where a > 0 is a constant, is known as an exponential function to the base a. If. > 1 then the graph looks like this: y = , a > 1. ( 1,a ) 1 This is sometimes called a growth.
The Relationship between Exponentials and Logarithms To understand a logarithm, you can think of it as the inverse of an exponential function. While an exponential function such as =5 tells you what you get when you multiply 5 by itself times, the corresponding logarithm, =log5( ), asks the opposite question: how many
Exponentials and Logarithms. This chapter is devoted to exponentials like 2x and 10x and above all ex: The goal is to understand them, differentiate them, integrate them, solve equations with them, and invert them (to reach the logarithm).
1 EXPONENTS AND LOGARITHMS WHAT YOU NEED TO KNOW • The rules of exponents: • ma m× an = a +n • a a a m n = mn • (am)n mn= a • aa m n n m • a a n n − = 1 • an × nb = (ab)n • a b a b n n n = ⎛ ⎝⎜ ⎛ ⎝ ⎞ ⎠⎟ ⎞ ⎠ • The relationship between exponents and logarithms: • ab=⇔b xb g a where a is called the ...
In this booklet we will demonstrate how logarithmic functions can be used to linearise certain functions, discuss the calculus of the exponential and logarithmic functions and give some useful applications of them.
Many mathematical models of reallife situations use - exponentials and logarithms. It is important to become familiar with using the laws of logarithms to help solve equations.
