ISRO | ISRO CS 2017 | Question 10

If log(base a) 2 = x and log(base a) 8 = y, what is the value of log(base a) 16? 

(A)

2x + y 

(B)

2x – y 

(C)

x + y 

(D)

4x

Answer: (C) (D)
Explanation:

We know that log(base a) 2 = x and log(base a) 8 = y. 
We need to find the value of log(base a) 16. 
Let’s express 16 as a power of 2: {16 = 2^4} 
Now, we can rewrite log(base a) 16 using the properties of logarithms: 
log(base a) 16 = log(base a) (2^4) 
Using the power rule of logarithms, we can bring the exponent out front: 
log(base a) 16 = 4 * log(base a) 2 
Substituting the given values, we have: log(base a) 16 = 4x 
The correct answer is 4x.

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