Simultaneous Quadratic Exponential and Logarithmic Equations INTRODUCTION Examining

Simultaneous, Quadratic, Exponential and Logarithmic Equations

INTRODUCTION �Examining equations where there is more than one unknown quantity – simultaneous equations. �Distinction between linear and quadratic equations �Principles and rules of logarithms and exponential values, and learn how to solve equations using them

SIMULTANEOUS EQUATIONS �In practice, many situations will arise when there is more than one unknown. �If an equation involves two unknown quantities, we may find any number of pairs of values to satisfy it

�Where the unknowns are denominators

�Forming simultaneous equations from single equations

FORMULATING PROBLEMS AS SIMULTANEOUS EQUATIONS

QUADRATIC EQUATIONS �By contrast, a quadratic equation is one that contains the square of the unknown number, but no higher power �One of the features of quadratic equations is that, usually, they cannot be solved definitively. There are generally two possible values for the unknown. �A second feature, reflecting this, is that when we draw a graph of the outcome of a quadratic equation for all the possible values of the

Solving Quadratic Equations by Formula

The Exponential Number e �There is a particular constant used in many mathematical calculations whose value (to seven decimal places) is 2. 7182818. This value occurs so frequently when mathematics is used to model physical and economic phenomena that it is convenient to write it simply as e; it is known as the exponential constant or exponential number

Logarithms �A logarithm (also known simply as a log) is used to write an expression involving powers. �In essence, a logarithm is the power to which a fixed number (base) must be raised in order to produce a given number.