Question:
If log 2(5+log3a)=3 and log5(4a+12+log2b) = 3, then a+b is equal to
If log 2(5+log3a)=3 and log5(4a+12+log2b) = 3, then a+b is equal to
Updated On: Jul 29, 2025
- 67
- 40
- 32
- 59
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The Correct Option is D
Solution and Explanation
We are given two logarithmic equations and need to find the sum of a and b. Let's solve them step-by-step.
- Consider the first equation:
log2(5+log3a)=3
This implies:
23 = 5 + log3a
8 = 5 + log3a
log3a = 8 - 5 = 3
Therefore, a = 33 = 27
- Next, consider the second equation:
log5(4a+12+log2b)=3
This implies:
53 = 4a + 12 + log2b
125 = 4a + 12 + log2b
Using value of a from step 1:
125 = 4(27) + 12 + log2b
125 = 108 + 12 + log2b
125 = 120 + log2b
log2b = 125 - 120 = 5
Therefore, b = 25 = 32
- Summing values of a and b:
a + b = 27 + 32 = 59
Thus, the value of a + b is 59.
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