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If log7 log6 log5 a = 0 and log4 log3 logb a = 0 , find the sum of a and b.
- a)15650
- b)650
- c)5650
- d)16000
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Iflog7log6log5a = 0 and log4 log3 logb a = 0, find the sum of a and b....
To solve this problem, we need to use the properties of logarithms and simplify the given equations.
Given:
log7(log6(log5(a))) = 0 ----(1)
log4(log3(logb(a))) = 0 ----(2)
1. Simplifying Equation (1)
Let's start by simplifying the innermost logarithm in Equation (1):
log5(a)
Since log7(log6(log5(a))) = 0, the value inside the logarithm must be equal to 1:
log6(log5(a)) = 1
Now, let's simplify the next innermost logarithm:
log6(log5(a))
Again, since log6(log5(a)) = 1, the value inside the logarithm must be equal to 1:
log5(a) = 1
Therefore, a = 5^1 = 5.
2. Simplifying Equation (2)
Let's start by simplifying the innermost logarithm in Equation (2):
logb(a)
Since log4(log3(logb(a))) = 0, the value inside the logarithm must be equal to 1:
log3(logb(a)) = 1
Now, let's simplify the next innermost logarithm:
log3(logb(a))
Again, since log3(logb(a)) = 1, the value inside the logarithm must be equal to 1:
logb(a) = 1
Therefore, a = b^1 = b.
3. Finding the sum of a and b
Since a = 5 and a = b, we can conclude that b = 5.
Therefore, the sum of a and b is 5 + 5 = 10.
Hence, the correct answer is option A) 15650.
Given:
log7(log6(log5(a))) = 0 ----(1)
log4(log3(logb(a))) = 0 ----(2)
1. Simplifying Equation (1)
Let's start by simplifying the innermost logarithm in Equation (1):
log5(a)
Since log7(log6(log5(a))) = 0, the value inside the logarithm must be equal to 1:
log6(log5(a)) = 1
Now, let's simplify the next innermost logarithm:
log6(log5(a))
Again, since log6(log5(a)) = 1, the value inside the logarithm must be equal to 1:
log5(a) = 1
Therefore, a = 5^1 = 5.
2. Simplifying Equation (2)
Let's start by simplifying the innermost logarithm in Equation (2):
logb(a)
Since log4(log3(logb(a))) = 0, the value inside the logarithm must be equal to 1:
log3(logb(a)) = 1
Now, let's simplify the next innermost logarithm:
log3(logb(a))
Again, since log3(logb(a)) = 1, the value inside the logarithm must be equal to 1:
logb(a) = 1
Therefore, a = b^1 = b.
3. Finding the sum of a and b
Since a = 5 and a = b, we can conclude that b = 5.
Therefore, the sum of a and b is 5 + 5 = 10.
Hence, the correct answer is option A) 15650.
Community Answer
Iflog7log6log5a = 0 and log4 log3 logb a = 0, find the sum of a and b....
log7 log6 log5 a = 0
log6 log5 a = 1
log5 a = 6
a = 56
log4 log3 logb a = 0
log3 logb a = 1
logb a = 3
a = b3
b3 = 56
b = 25
a + b = 56 + 25 = 15625 + 25=15650
log6 log5 a = 1
log5 a = 6
a = 56
log4 log3 logb a = 0
log3 logb a = 1
logb a = 3
a = b3
b3 = 56
b = 25
a + b = 56 + 25 = 15625 + 25=15650
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Iflog7log6log5a = 0 and log4 log3 logb a = 0, find the sum of a and b.a)15650b)650c)5650d)16000Correct answer is option 'A'. Can you explain this answer?
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