Step 2: Solve forx
3 x= 81or 3 x= 1. However 3 x= 1 is undefined, so:
3 x= 81
3 x= 3^4
x= 4Thereforex= 4
Worked example 12: Solving equations by factorising a trinomial
QUESTION
Solve forp:
p 13 p
(^12)
- 36 = 0
SOLUTION
Step 1: Rewrite the equation
We notice that
(
p12 )^2
=pso we can rewrite the equation as:(
p1
2) 2
13 p1(^2) + 36 = 0
Step 2: Factorise as a trinomial
(
p
(^12)
9
) (
p(^12)
4
)
= 0
Step 3: Solve to find both roots
p(^12)
9 = 0 or p
(^12)
4 = 0
p
(^12)
= 9 p
(^12)
= 4
(
p
12 )^2
= (9)^2
(
p12 )^2
= (4)^2
p = 81 p = 16Thereforep= 81orp= 16.
Worked example 13: Solving equations by factorisation
QUESTION
Solve forx:
2 x 24 x= 0
54 2.4. Exponential equations