Use the Laws of logarithms to rewrite the expression log(base 2)(11x(x-9))

in a form with no logarithm of a product, quotient or power.
After rewriting we will have:

log(base 2)A+log(base 2)x+log(base 2)f(x)
What is A and what is f(x)?

To rewrite the expression log(base 2)(11x(x-9)) using the laws of logarithms, we can start by breaking it down step by step.

First, we have the product inside the logarithm, 11x(x-9). We can use the product rule of logarithms, which states that log(base a)(xy) = log(base a)x + log(base a)y.

So, we can split the expression into two separate logarithms:
log(base 2)(11x) + log(base 2)(x-9)

Next, we can simplify further. For the first term, log(base 2)(11x), we don't have any additional simplification we can do. However, for the second term, log(base 2)(x-9), there's still a subtraction inside the logarithm.

To further simplify this, we can use the quotient rule of logarithms, which states that log(base a)(x/y) = log(base a)x - log(base a)y. In this case, we can think of (x-9) as x divided by 9. So, we have:

log(base 2)(11x) + log(base 2)(x) - log(base 2)(9)

Now, we can simplify the expression inside the logarithms:
log(base 2)(11x) + log(base 2)(x) - log(base 2)(9)

Finally, we can rewrite the expression in the desired form by combining the logarithms using the sum rule of logarithms. The sum rule states that log(base a)x + log(base a)y = log(base a)(xy).

So, applying the sum rule, we can rewrite the expression as:
log(base 2)(11x*x) - log(base 2)(9)

Now, we have the expression in the form log(base 2)A + log(base 2)x + log(base 2)f(x), where A = 11x*x and f(x) = 9.