Provide an appropriate response.Why can the equation log6(x - 7) = log6(7 - x) be said to have no solution?
What will be an ideal response?
Answers may vary. One possibility: To solve an equation of the form 
one attempts to solve the related equation f(x) = g(x), which in this case is the equation 
Though this related equation has a solution, there is a quick way to see that it will not solve the original logarithmic equation. By inspection, (x - 7) and (7 - x) are negatives. For them to be equal, either one is negative, or both are equal to 0. Since log u is only defined when 
inserting the solution of the related equation into the original equation would make at least one of the logarithms undefined. Thus, there is no solution to the original logarithmic equation.
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