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Directions: Express the following exponential functions in logarithmic form. ( log2x = y)
1. 10^8 = 100, 000, 000
2. 10^-4 = 0.0001
3. 10^-7 = 0.0000001
4. 5^3 = 125
5. 3^-2 = 1/9
6. 3^0 = 1
7. 5^-3 = 0.008
8. 20^4 = 160,000
9. 9^-1/2 = 1/3
10. 5^-3 = 1/125
Answers
Answer:Examples on convert Exponentials and Logarithms
1. Convert the following exponential form to logarithmic form:
(i) 104 = 10000
Solution:
104 = 10000
⇒ log10 10000 = 4
(ii) 3-5 = x
Solution:
3-5 = x
⇒ log3 x = -5
(iii) (0.3)3 = 0.027
Solution:
(0.3)3 = 0.027
⇒ log0.3 0.027 = 3
2. Convert the following logarithmic form to exponential form:
(i) log3 81 = 4
Solution:
log3 81 = 4
⇒ 34 = 81, which is the required exponential form.
(ii) log8 32 = 5/3
Solution:
log8 32 = 5/3
⇒ 85/3 = 32
(iii) log10 0.1 = -1
Solution:
log10 0.1 = -1
⇒ 10-1 = 0.1.
3. By converting to exponential form, find the values of following:
(i) log2 16
Solution:
Let log2 16 = x
⇒ 2x = 16
⇒ 2x = 24
⇒ x = 4,
Therefore, log2 16 = 4.
(ii) log3 (1/3)
Solution:
Let log3 (1/3) = x
⇒ 3x = 1/3
⇒ 3x = 3-1
⇒ x = -1,
Therefore, log3(1/3) = -1.
(iii) log5 0.008
Solution:
Let log5 0.008 = x
⇒ 5x = 0.008
⇒ 5x = 1/125
⇒ 5x = 5-3
⇒ x = -3,
Therefore, log5 0.008 = -3.
4. Solve the following for x:
(i) logx 243 = -5
Solution:
logx 243 = -5
⇒ x-5 = 243
⇒ x-5 = 35
⇒ x-5 = (1/3)-5
⇒ x = 1/3.
(ii) log√5 x = 4
Solution:
log√5 x = 4
⇒ x = (√5)4
⇒ x = (51/2)4
⇒ x = 52
⇒ x = 25.
(iii) log√x 8 = 6
Solution:
log√x 8 = 6
⇒ (√x)6 = 8
⇒ (x1/2)6 = 23
⇒ x3 = 23
⇒ x = 2.
Step-by-step explanation: