Question

If log 2(5+log3a)=3 and log5(4a+12+log2b) = 3, then a+b is equal to

• A. 67
• B. 40
• C. 32
• D. 59

Answer 1

The Correct Option is D

We are given two logarithmic equations and need to find the sum of a and b. Let's solve them step-by-step.

1. Consider the first equation: 
    

log₂(5+log₃a)=3

This implies:
2³ = 5 + log₃a
8 = 5 + log₃a
log₃a = 8 - 5 = 3

Therefore, a = 3³ = 27

1. 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

1. Summing values of a and b:

a + b = 27 + 32 = 59

Thus, the value of a + b is 59.