Analysis and Approaches for IBDP Maths Ebook 1 | Page 47

14
Paper 1 Section A – Solving exponential
and logarithmic equations
Front Page
Example
Solve log3x�log 3( x�8) � 2 , for x �� 8.
Solution
[7]
4
log x�log ( x�8) � 2
3 3
log xx� ( 8) � 2
(A1) for correct formula
3
2
log
3( x �8 x) � 2
2 2
x �8x� 3
(A1) for valid approach
2
x �8x�9 � 0
A1
( x�9)( x�1) � 0
(M1) for factorization
x �� 9 (Rejected) or x � 1
A1
�x
� 1
A2 N3
[7]
Exercise 14
1. Solve log
216x�log 2(2 � x) � 4 , for 0�x
� 2.
2
x 2(3x�4)
2. Solve 2 �2 � 8.
[7]
2
�8x�
x �
3. Consider f( x) � log
k � �, for 0�x
� 8, where k � 0 . The equation f( x) � 2 has
� 4 �
exactly one solution. Find the value of k .
[7]
2
6
4. Consider f ( x) �log 3(6 x � kx ) , for 0 � x � , where k � 0 . The equation f( x) � 1 has
k
two distinct real solutions. Find the range of values of k .
[7]
[5]
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