Jerome solved the equation by graphing. the log base 2 of x plus log sub 2 of open paren x minus 2 close paren is equal to 3 Which of the following shows the correct system of equations and solution?

Using the change-of-base rule, each base-2 logarithm can be written as a common logarithm divided by log 2. So the system is y₁ = log x/log 2 + log(x − 2)/log 2 and y₂ = 3. To find their intersection, combine the original logarithms: log₂[x(x − 2)] = 3, so x(x − 2) = 8. Solving gives x = 4 or x = −2, but x must be greater than 2 for the logarithms to be defined, so x = 4; this is choice C.

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