Consider the equation $\log _{2} x+\log _{2}(x-4)=5$.
(a) Solve the equation analytically. If there is an extraneous value, what is it?
(b) To support the solution in part (a), we may graph $y_{1}=\log _{2} x+\log _{2}(x-4)-5$ and find the $x$-intercept.
Write an expression for $y_{1}$ using the change-of-base rule with base 10 , and graph the function to support the solution from part (a).
(c) Use the graph to solve the inequality $\log _{2} x+\log _{2}(x-4)

Question

Consider the equation $\log _{2} x+\log _{2}(x-4)=5$.
(a) Solve the equation analytically. If there is an extraneous value, what is it?
(b) To support the solution in part (a), we may graph $y_{1}=\log _{2} x+\log _{2}(x-4)-5$ and find the $x$-intercept.
Write an expression for $y_{1}$ using the change-of-base rule with base 10 , and graph the function to support the solution from part (a).
(c) Use the graph to solve the inequality $\log _{2} x+\log _{2}(x-4)<5$.

Quizplus · Accepted Answer

The Answer of Consider the equation $\log _{2} x+\log _{2}(x-4)=5$.
(a) Solve the equation analytically. If there is an extraneous value, what is it?
(b) To support the solution in part (a), we may graph $y_{1}=\log _{2} x+\log _{2}(x-4)-5$ and find the $x$-intercept.
Write an expression for $y_{1}$ using the change-of-base rule with base 10 , and graph the function to support the solution from part (a).
(c) Use the graph to solve the inequality $\log _{2} x+\log _{2}(x-4)<5$.

Consider the Equation log⁡2x+log⁡2(x−4)=5\log _{2} x+\log _{2}(x-4)=5log2​x+log2​(x−4)=5 (A) Solve the Equation Analytically

Consider the Equation $\log _{2} x+\log _{2}(x-4)=5$
(A) Solve the Equation Analytically