Essential Mathematics for Economics and Business 4 th

Essential Mathematics for Economics and Business, 4 th Edition INDICES AND LOGS www. wiley. com/college/Bradley © John Wiley and Sons 2013

Review indices Relationship between indices and logs Logs: The log of a number…. Rules for Logs Some Worked Examples www. wiley. com/college/Bradley © John Wiley and Sons 2013

The rules for indices Rule 1: To multiply numbers with the same base, add the indices. Example by Indices rule Same example by arithmetic Rule 2: To divide numbers with the same base, subtract the index of the divisor. Rule 3: To raise an exponential to a power, multiply the indices. www. wiley. com/college/Bradley © John Wiley and Sons 2013

The relationship between indices and logs number = base. Power log base (number) = Power A base is always base Index form: www. wiley. com/college/Bradley logs are powers Log form: © John Wiley and Sons 2013

On the calculator…. Logs to base 10 log 10 N is written as log. N log 1020 is written as log 20 =1. 3010 Logs to base e loge. N is written as ln. N loge 20 is written as ln 20 =2. 9957 www. wiley. com/college/Bradley © John Wiley and Sons 2013

The rules for logs Rule 1: Add Example ☺ Rule 2: Subtract. ☺ Rule 3: Log of an exponential ☺ Rule 4: change of base rule. ☺ Note: log 10(10)=1 www. wiley. com/college/Bradley © John Wiley and Sons 2013

The relationship between indices and logs To go from index to log number = base Power log base (number) = Power A base is always base To go from log to index reverse the process log base (number) = Power number = base. Power www. wiley. com/college/Bradley © John Wiley and Sons 2013

The relationship between indices and logs To go from index to log number = base Power log base (number) = Power A base is always base To go from log to index reverse the process number = base. Power log base (number) = Power www. wiley. com/college/Bradley © John Wiley and Sons 2013

Solve equations using the rules for indices and logs WE 4. 17(a) Go from log to index Alternatively Take logs of each side Note: log 10(10)=1 www. wiley. com/college/Bradley © John Wiley and Sons 2013

Solve equations using the rules for indices and logs WE 4. 21(a) Divide each side by 3 Take logs www. wiley. com/college/Bradley of each side © John Wiley and Sons 2013

Solve equations using the rules for indices and logs WE 4. 22(a) Go from log to index www. wiley. com/college/Bradley © John Wiley and Sons 2013

Solve equations using the rules for indices and logs WE 4. 22(b) Go from log to index www. wiley. com/college/Bradley Solve the quadratic © John Wiley and Sons 2013

Further information https: //www. khanacademy. org/math/algebra 2/exponentialand-logarithmic-functions Other functions(circle, ellipse, hyperbola): https: //www. khanacademy. org/math/precalculus/conicsprecalc www. wiley. com/college/Bradley © John Wiley and Sons 2013

Rectangular hyperbolic functions Standard form vs y=1/x See lecture notes. www. wiley. com/college/Bradley © John Wiley and Sons 2013