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Question 27 :If log_{2}(5 + log_{3}a) = 3 and log_{5}(4a + 12 + log_{2}b) = 3, then a + b is equal to

- 32
- 59
- 67
- 40

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We know that if log_{q}p = r then p = q^{r}

Given log_{2}(5 + log_{3}a) = 3

5 + log_{3}a = 23

log_{3}a = 3

a = 3^{3} = 27

Similarly, 4a + 12 + log_{2}b = 5^{3}

4a + log_{2}b = 113

log_{2}b = 5

b = 2^{5} = 32

a + b = 27 + 32 = **59**

The question is **"If log _{2}(5 + log_{3}a) = 3 and log_{5}(4a + 12 + log_{2}b) = 3, then a + b is equal to" **

Choice B is the correct answer.

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