Jerome solved the equation below by graphing.
log2(x) + log2(x-2) = 3
which of the following shows the correct system of equations and solution?

B. x = 4

Step-by-step explanation:

I can't speak to the first part of this question, as I don't totally have context for what they're asking, but we can solve for x using one of the laws of logarithms, namely:

Using this law, we can combine and rewrite our initial equation as

Remember that logarithms are simply another way of writing exponents. The logarithm is just another way of writing the fact . Keeping that in mind, we can express our logarithm in terms of exponents as

2³ = 8, so we can replace the left side of our equation with 8 to get

Moving the 8 to the other side:

We can now factor the expression on the right to find solutions for x:

The only option which agrees with our solution is B.

The answer is:

Step-by-step explanation:

We are given a logarithmic expression as:

As we know that:

Hence, we get the logarithmic expression as follows:

We know that we can get the system of equations as follows:

and

Hence, when we plot the graph for this system of equations we see that the point of intersection of the graph is: (4,3)

Hence, the solution is the x-value of the point of intersection of the two equations.

Hence, x=4 is the solution.

Hence, the correct option is:

42

step-by-step explanation: