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If log2(5 + log3 a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is equal to
(2018)
- a)40
- b)67
- c)59
- d)32
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If log2(5 + log3 a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is ...
5 + log3 a = 23 = 8 ⇒ log3a = 3 ⇒ a = 27 Similarly, 4a + 12 + log2b = 53 = 125
Since a = 27, 4(27) + 12 + log2b = 125
⇒ log2b = 5 ⇒ b = 32.
∴ a + b = 27 + 32 = 59
Since a = 27, 4(27) + 12 + log2b = 125
⇒ log2b = 5 ⇒ b = 32.
∴ a + b = 27 + 32 = 59
Most Upvoted Answer
If log2(5 + log3 a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is ...
Solution:
Given, log2(5 log3 a) = 3
Using the property of logarithm, we get
5 log3 a = 23
5 log3 a = 8
log3 a = 3/5
a = 35/5 = 243
Given, log5(4a 12 log2 b) = 3
Using the property of logarithm, we get
4a 12 log2 b = 53
4a 12 log2 b = 125
4a log2 b = 113
a log2 b^4 = 113
log2 (a b^4) = log2 a + 4 log2 b = 113
Substituting the value of a, we get
log2 (243 b^4) = log2 243 + 4 log2 b = 5 + 4 log2 b
log2 (243 b^4) = 5 + 4 log2 b = log2 32 + log2 b^4
243 b^4 = 32b^4
b^4 = 81
b = 3
Therefore, a b = 243 3 = 729
Hence, the correct answer is option C.
Given, log2(5 log3 a) = 3
Using the property of logarithm, we get
5 log3 a = 23
5 log3 a = 8
log3 a = 3/5
a = 35/5 = 243
Given, log5(4a 12 log2 b) = 3
Using the property of logarithm, we get
4a 12 log2 b = 53
4a 12 log2 b = 125
4a log2 b = 113
a log2 b^4 = 113
log2 (a b^4) = log2 a + 4 log2 b = 113
Substituting the value of a, we get
log2 (243 b^4) = log2 243 + 4 log2 b = 5 + 4 log2 b
log2 (243 b^4) = 5 + 4 log2 b = log2 32 + log2 b^4
243 b^4 = 32b^4
b^4 = 81
b = 3
Therefore, a b = 243 3 = 729
Hence, the correct answer is option C.
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If log2(5 + log3 a) = 3 and log5(4a + 12 + log2 b) = 3, then a + b is equal to(2018)a)40b)67c)59d)32Correct answer is option 'C'. Can you explain this answer?
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