Cambridge Additional Mathematics

Once we have the

same base we then

equate the indices.

116 Surds, indices, and exponentials (Chapter 4)

Anexponential equationis an equation in which the unknown occurs as part of the index or exponent.

For example: 2 x=8 and 30 £ 3 x=7 are both exponential equations.

There are a number of methods we can use to solve exponential equations.

These include graphing, using technology, and by usinglogarithms, which

we will study in Chapter 5. However, in some cases we can solve

algebraically.

If the base numbers are the same, we canequate indices.

If ax=ak then x=k.

For example, if 2 x=8 then 2 x=2^3. Thus x=3, and this is the

only solution.

Example 22 Self Tutor

Solve forx:

a 2 x=16 b 3 x+2= 271

a 2 x=16

) 2 x=2^4

) x=4

b 3 x+2= 271

) 3 x+2=3¡^3

) x+2=¡ 3

) x=¡ 5

Example 23 Self Tutor

Solve forx:

a 4 x=8 b 9 x¡^2 =^13

a 4 x=8

) (2^2 )x=2^3

) 22 x=2^3

) 2 x=3

) x=^32

b 9 x¡^2 =^13

) (3^2 )x¡^2 =3¡^1

) 3 2(x¡2)=3¡^1

) 2(x¡2) =¡ 1

) 2 x¡4=¡ 1

) 2 x=3

) x=^32

F Exponential equations

Remember that

a> 0.

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_04\116CamAdd_04.cdr Tuesday, 14 January 2014 2:28:36 PM BRIAN