If log4(x2 + x) – log4(x + 1) = 2 then the value of x is(a) 2(b) 3(c) 16(d) 8

To solve this problem, we can use the properties of logarithms.

The equation is: log4(x^2 + x) - log4(x + 1) = 2

According to the properties of logarithms, the difference of two logarithms is the logarithm of the quotient. So, we can rewrite the equation as:

log4[(x^2 + x) / (x + 1)] = 2

This means that (x^2 + x) / (x + 1) = 4^2 = 16

So, we have the equation x^2 + x = 16x + 16

Rearranging terms, we get x^2 - 15x + 16 = 0

This is a quadratic equation, which we can solve by factoring:

(x - 1)(x - 16) = 0

Setting each factor equal to zero gives the solutions x = 1 and x = 16.

However, we must check these solutions in the original equation to make sure they are valid. If we plug x = 1 into the original equation, we get log4(2) - log4(2) = 2, which is not true. So, x = 1 is not a solution.

If we plug x = 16 into the original equation, we get log4(272) - log4(17) = 2, which is true. So, x = 16 is a solution.

Therefore, the correct answer is (c) 16.