Algebra 06 : Class Notes || IPMAT Pro 2025.pdf

Class 6 algebra

1. TARGET CAT 2024
Quant : Algebra
Logarithm
Lecture No.- 0
6
By- VINIT KAKRIYA SIR
PRO/MASTERQUEST
TARGET IPMAT 2025

2. Recap of Previous Lecture :

3. Recap of Previous Lecture :

4. 1)Concepts & Numerical based on ‘Inequalities’
2)Concepts & Numerical based on ‘Logarithm’
3)Problems for Practice & IPMAT PYQs
to be covered

5. Quick Revision for Quadratic Equation : (Special Case)

6. Quick Revision for Quadratic Equation : (Special Case)

7. QUESTION- 1
#Q. x
2
+x+1>0, Find the values of x that satisfies the equation.

8. QUESTION- 2
#Q. −??????
2
+??????−1>0, Find the values of x that satisfies the equation.

9. QUESTION- 3
#Q.
??????
2
+??????+1??????
2
+5??????+6
??????
2
−3??????
≥0

10. QUESTION- 4
#Q. If x ∈ (a, b) satisfies the inequality
?????? − 3
??????
2
+3??????+2
≥ 1, then the largest possible value of
(b – a) is [IPMAT Indore PYQ]
3A
1B
2C
No real values of x satisfies the inequalityD

11. Logarithm

12. Logarithm :

13. Logarithm :

14. Logarithm :

15. Logarithm :

16. Logarithm :

17. Logarithm :

18. Logarithm :

19. Logarithm :
Important Properties:
1. log
a b =
��?????? �
��?????? �
2. log
a b =
1
��??????��

3. ��??????
�� + ��??????
�� = ��??????
��� 4. ��??????
�� - ��??????
�� = ��??????
�
�
�
5. log
�1 = 0 6. log
a a = 1
7. ��??????
��
�
= m. ��??????
�� 8. log
??????
??????�=
1
�
��??????
??????�

9. Conversion of Logarithmic form into Exponential form:
log
a b = x b = a
x
10. Conversion of Exponential form into Logarithmic form:
p = q
r
log
q p = r
11. �
��??????��
=�

20. QUESTION- 1
#Q.Log (x – 13) + 3 Log 2 = Log (3x + 1)
A
B
C
D
20
21
22
24

21. QUESTION- 2
#Q.Log (75/16) - 2 Log (5/9) + Log (32/243) reduces to
A
B
C
D
2log2
5log2
log2
4log2

22. QUESTION- 3
#Q.Solve : log7
�
5
�
3
−log
�
1
2
�
2
A
B
C
D
2
0.2
5
-5

23. QUESTION- 4
#Q.Find the sum of all the possible values of x which satisfy the following equation.
log
??????5??????+14=2
A
B
C
D
7
-2
5
10

24. QUESTION- 5
#Q.Solve :
A
B
C
D
x + 1
??????
2
+?????? + 1
??????
2
−?????? + 1
x − 1
5
log
5??????
3
−1
3
log
3??????
−2log
��

25. QUESTION- 6
#Q.Log
2 [Log
3 (Log
2 x)] = 1, Then x =?
A
B
C
D
128
256
512
None of these

26. QUESTION- 7
#Q.If Log a =
??????�?????? �
2
=
??????�?????? �
5
, then the value of a
4
b
3
c
-2
is
2A
B
C
D
1
0
−1

27. 2 Mins Summary
1)Concepts & Numerical based on ‘Inequalities’
2)Concepts & Numerical based on ‘Logarithm’
3)Problems for Practice & IPMAT PYQs

28. Thank
You