using calculator in solving indices and logarithm in a simple way.

1. INDICES
• It is of the form ax
• Where ‘a’ is the base
• X is the power/exponent/index
• ‘𝑥□’ is the symbol for power on the calculator.

2. Base with positive exponent
Evaluate 23
SOLUTION
Type the question
press [𝑥□
] and the fill the boxes
ANS: 8

3. Evaluate
1.(√3)4
2.(2
5
)2
3.34

4. A BASE WITH A NEGATIVE EXPONENT
Evaluate
1. 3-3
2. 0.125-2
3. 9-2
NOTE: Follows the same procedure as the first example.

5. A BASE WITH A FRACTION EXPONENT
Evaluate the ff:
1. 4
1
2
2. 81
1
2
3. 32
2
5

6. A FRACTION WITH EXPONENT
1.
8
27
−2
3
2.
27
64
−2
3
3. 3−3
× 8
27
−2
3 × 0.252
4.
7−2×73 ×7−5
7−6 ×73

7. INDICES EQUATION
Type the question as it is using [ALPHA] to get your
variable (i.e. x or y) and ‘‘=’’.
Press [SHIFT] and [CALC] to command the calculator
to solve
Press [=] to get your answer (takes a while depending
on the question)

8. EXAMPLES

9. If 2x = 8 find the value of x.
SOLUTION
Type the question
Press [𝑥□
] 2(Base) and x (exponent)
Press [ALPHA] and then [CALC]
Press 8
Press [SHIFT] and then [CALC]
Finally press [=] to get your answer
ANS: X = 3

10. If 42−𝑥
× 16𝑥+1
= 64, find the value of m.
If 21−2𝑠
= 16, find the value of s.
(1
3
)3𝑥
= 81
−3
4 find the value of x

11. LOGARITHM
Calculator is in standard base. i.e base 10
It of the form 𝑙𝑜𝑔𝑎b = c
Then b = 𝑎𝑐

12. NOTE
If the question is in base 10 then press
log alone.
If the question is not in standard base
(i.e. not base 10) the press 𝒍𝒐𝒈□▯

13. Simplify 𝑙𝑜𝑔10100.
HINT: what number should the base(in this case 10) be raised to get 100.
SOLUTION
1. Press [log]
2. Type 100
3. Press [=]
ANS: 10

14. Simpliify 𝑙𝑜𝑔2 8
SOLUTION
1. Press 𝑙𝑜𝑔□▯
2. Insert the base (2)
3. Press 8
4. Press [=]
Ans: x =3

15. EXAMPLES
1. Log 3 + log 5
2. 3 log 4 + log 2
3. 2 𝑙𝑜𝑔28 + 𝑙𝑜𝑔216 + 𝑙𝑜𝑔2 24

16. LOGARITHM EQUATION
Type the question as it is on the calculator
Command the calculator to solve the question
by pressing [SHIFT] and [CALC]
Press [=]

17. EXAMPLES
If 𝑙𝑜𝑔2 8 = x find the value of x.
SOLUTION
1. Press [𝑙𝑜𝑔□▯] and inseret the base(2) and then 8
2. Press [ALPHA] and [CALC] (to get ‘‘=’’)
3. press x
4. Press [SHIFT] and [CALC]
5. Press [=]

18. X = 3

19. find the value of x.
1.𝑙𝑜𝑔𝑥27 = 3
2.𝑙𝑜𝑔√3(27√3) = x
3.3𝑙𝑜𝑔10𝑥 + 𝑙𝑜𝑔103 = 𝑙𝑜𝑔1081
4.𝑙𝑜𝑔22x + 𝑙𝑜𝑔24 = 2

20. ANSWER
1.x = 3
2.x = 7
3.x = 3
4.x = 0.125 or 1
8