Cambridge International Mathematics

SOLVING EXPONENTIAL EQUATIONS GRAPHICALLY

In many exponential equations we cannot easily make the base numbers on both sides the same. For example,

if 3 x=6we cannot easily write 6 with a base number of 3.

We can solve these types of exponential equations using a graphics calculator, using the methods learnt in

Chapter 23.

Discovery 3 Solving exponential equations graphically

#endboxedheading

Consider the exponential equation 3 x=6.

Since 31 =3and 32 =9, the solution forxmust lie between 1 and 2.

Agraphics calculatorcan be used to solve this equation by drawing the graphs of y=3x and

y=6 and finding theirpoint of intersection. To find out how to do this, consult the instructions on

pages 23 to 24.

Alternatively, click on the icon to obtain a graphing package.

1 Draw the graph of y=3x.

2 Draw the graph of y=6 on the same set of axes.

3

4 Solve forx, correct to 3 decimal places:

a 3 x=10 b 3 x=30 c 3 x= 100

d 2 x=12 e 5 x=40 f 7 x=42

If using a calculator you may have to change the viewing window scales.

Example 6 Self Tutor

Solve 2 x=10correct to 3 decimal places.

We could also

ploty=2x

and y=10on

the same set of

axes.

2 x=10has the same solutions as

2 x¡10 = 0.

Thex-intercept¼ 3 : 322

) x¼ 3 : 322

GRAPHING

PACKAGE

O

y

x

» 3. 322

y= 2 x- 10

572 Exponential functions and equations (Chapter 28)

Find the coordinates of the point of intersection of the graphs.

What to do:

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_28\572IGCSE01_28.CDR Friday, 31 October 2008 9:58:00 AM PETER