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If log 360 = a, log 300 = b find the value of log 432 in terms of a and b
  • a)
    2b - a
  • b)
    2a - b
  • c)
    a - b
  • d)
    b - a
Correct answer is option 'B'. Can you explain this answer?
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If log 360 = a, log 300 = b find the value of log 432 in terms of a an...
log 360 = a 
log 300 = b  
log 432 = ?
3 log 2 + 2 log 3 + log 5 = a  (....i)
2 log 2 + log 3 + 2 log 5 = b (....ii)
log 432 = 4 log 2 +3 log 3
2i - ii
4 log 2 + 3 log 3 = 2a - b
log 432 = 2a - b
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Most Upvoted Answer
If log 360 = a, log 300 = b find the value of log 432 in terms of a an...
To find the value of log 432 in terms of a and b, we can use logarithmic properties and algebraic manipulation.

Given:
log 360 = a
log 300 = b

We need to find:
log 432 in terms of a and b

Solution:
Use the logarithmic property log (a * b) = log a + log b

We can express 432 as a product of its prime factors:
432 = 2^4 * 3^3

Now, let's express 432 in terms of its prime factors:
log 432 = log (2^4 * 3^3)

Using the logarithmic property log (a * b) = log a + log b:
log 432 = log (2^4) + log (3^3)

Simplify the logarithms using the logarithmic property log (a^b) = b * log a:
log 432 = 4 * log 2 + 3 * log 3

We know that log 300 = b, so substitute the value of b:
log 432 = 4 * log 2 + 3 * log 3
= 4 * log 2 + 3 * log 3 + log 1 - log 1
= 4 * log 2 + 3 * log 3 + log (2 * 1) - log 1
= 4 * log 2 + 3 * log 3 + log 2 + log 1 - log 1
= 4 * log 2 + log 2 + 3 * log 3

Now, we know that log 360 = a, so substitute the value of a:
log 432 = 4 * log 2 + log 2 + 3 * log 3
= 5 * log 2 + 3 * log 3

Therefore, log 432 in terms of a and b is 5a + 3b.

Hence, the correct answer is option B, 2a - b.
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Given sequence: 3, 11, 34, 69, 131, 223To find the pattern in the sequence, let's calculate the differences between consecutive terms:11 - 3 = 834 - 11 = 2369 - 34 = 35131 - 69 = 62223 - 131 = 92The differences between consecutive terms are not following a consistent pattern. Therefore, the given sequence does not have a simple arithmetic or geometric progression.However, if we observe the differences between the differences, we can see a pattern:23 - 8 = 1535 - 23 = 1262 - 35 = 2792 - 62 = 30The differences between the differences are increasing by a constant value. This indicates that the given sequence might have a polynomial pattern.To find the polynomial pattern, we can use the method of finite differences. Let's calculate the second differences:15 - 12 = 312 - 27 = -1527 - 30 = -3The second differences are not constant. Therefore, the given sequence might have a polynomial of degree 2.Let's assume the polynomial is of the form ax^2 + bx + c. Substituting the given terms into the polynomial, we can form the following equations:1. 3a + b + c = 32. 9a + 3b + c = 113. 16a + 4b + c = 34Solving these equations, we get a = 1, b = 2, and c = 0.Therefore, the polynomial pattern for the given sequence is x^2 + 2x.Now, let's find the missing terms in the sequence

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If log 360 = a, log 300 = b find the value of log 432 in terms of a and ba)2b - ab)2a - bc)a - bd)b - aCorrect answer is option 'B'. Can you explain this answer?
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