46: Indices and Laws of Logarithms © Christine Crisp “Teach A Level Maths” Vol. 1:...

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Transcript of 46: Indices and Laws of Logarithms © Christine Crisp “Teach A Level Maths” Vol. 1:...

  • Module C2"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

  • Equations with unknown indices are solved using logarithms. We will see what a logarithm is and develop some rules that help us to solve equations.

  • e.g. How would you solve

  • Our calculators give us the value of the logarithm of 75 with a base of 10.

  • To solve an equation where the index is unknown, we can use logarithms.

  • Solution:

  • Generalizing this,In the exercise, we saw thatThis relationship is also true changing from the log form to the index form,

  • Generalizing this,In the exercise, we saw thatThis relationship is also true changing from the log form to the index form,

  • Generalizing this,This relationship is also true changing from the log form to the index form,In the exercise we used logs with a base of 10 but the definition holds for any base, soso,

  • BUT there are no values for logs with base 2 on our calculators so we cant find this as a simple number.We need to develop some laws of logs to enable us to solve a variety of equations with unknown indices or logs When the base, a, is 10, we found the equation is easy to solve.

  • Also,And,( from calculator )( from calculator )

  • Also,And,( from calculator )( from calculator )We get

  • The same reasoning holds for any base, a, so( the power to the front law of logs )

  • We take logsUsing the power to the front law, we can simplify the l.h.s.

  • Using the power to the front law:Divide by 100:Take logs:

  • SUMMARYThe Definition of a LogarithmTake logsThe Power to the Front law of logs:Use the power to the front lawRearrange to find x.Divide by n

  • Exercises( 2 d.p. )1. Solve the following equations giving the answers correct to 2 d.p.(a)(b)

  • Solution: Divide by 200:Exercises

  • The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.For most purposes the slides can be printed as Handouts with up to 6 slides per sheet.