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If log12 27 = a and log9 16 = b, then find log8 108.
- a)2(a + 3)/3b
- b)2(a + 3)/3a
- c)2(b + 3)/3a
- d)2(b + 3)/3b
Correct answer is option 'D'. Can you explain this answer?
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If log12 27 = a and log9 16 = b, then find log8 108.a)2(a + 3)/3bb)2(a...
Solution:
Given, log12 27 = a and log9 16 = b
We need to find log8 108
Let us try to express 108 in terms of powers of 8
108 = 8 × 8 × 8/2 = 83/2
Using the change of base formula, we can express log8 108 in terms of a and b
log8 108 = log12 108/log12 8 = log12 (83/2)/log12 2^3
We know that loga (bc) = loga b + loga c
Using this property, we can split the numerator of the above expression as follows:
log12 (83/2) = log12 (2^3 × 3/2) = log12 2^3 + log12 3/2
Substituting the values of a and b, we get:
log8 108 = (a + (2/3)b)/(3a)
= 2b/3a + 1
= 2(b+3)/3a
Hence, the correct option is D.
Given, log12 27 = a and log9 16 = b
We need to find log8 108
Let us try to express 108 in terms of powers of 8
108 = 8 × 8 × 8/2 = 83/2
Using the change of base formula, we can express log8 108 in terms of a and b
log8 108 = log12 108/log12 8 = log12 (83/2)/log12 2^3
We know that loga (bc) = loga b + loga c
Using this property, we can split the numerator of the above expression as follows:
log12 (83/2) = log12 (2^3 × 3/2) = log12 2^3 + log12 3/2
Substituting the values of a and b, we get:
log8 108 = (a + (2/3)b)/(3a)
= 2b/3a + 1
= 2(b+3)/3a
Hence, the correct option is D.
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If log12 27 = a and log9 16 = b, then find log8 108.a)2(a + 3)/3bb)2(a + 3)/3ac)2(b + 3)/3ad)2(b + 3)/3bCorrect answer is option 'D'. Can you explain this answer?
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