Logarithms

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Contents:

A Logarithms in basea [3.10]

B The logarithmic function [3.10]

C Rules for logarithms [3.10]

D Logarithms in base 10 [3.10]

E Exponential and logarithmic

equations [3.10]

InChapter 28we answered problems like the one above by graphing the exponential function and using

technology to find when the investment is worth a particular amount.

However, we can also solve these problems without a graph usinglogarithms.

We have seen previously that y=x^2 and y=

p

x areinverse functions.

For example, 52 =25and

p

25 = 5.

If y=ax then we say “xis the logarithm ofyin basea”, and write this as x= logay.

A LOGARITHMS IN BASE a [3.10]

Opening problem

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Tony invests$8500fornyears at 7 :8%p.a. compounding annually. The interest rate is fixed for the

duration of the investment. The value of the investment afternyears is given byV= 8500£(1:078)n

dollars.

Things to think about:

a How long will it take for Tony’s investment to amount to$12 000?

b How long will it take for his investment to double in value?

Logarithms were created to be theinverse of exponential functions.

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Y:\HAESE\IGCSE01\IG01_31\625IGCSE01_31.CDR Tuesday, 18 November 2008 11:10:27 AM PETER