Logarithmic equations and inequalities

9000003806

Level: 
B
In the following list identify an equation such that neither \(x = 5\) nor \(x = 3\) is the solution of this equation.
\(\log _{3}(1 - x) =\log _{3}(x + 16 - x^{2})\)
\(\log (54 - x^{3}) = 3\cdot \log x\)
\(\log _{5}(x^{2} - 17) =\log _{5}(x + 3)\)
\(\log (x - 2) -\log (4 - x) = 1 -\log (13 - x)\)

9000003808

Level: 
B
Identify one statement which is true for the following equation. \[ \log (x - 13) -\log (x - 3) = 1 -\log 2 \]
The equation does not have a solution.
The equation has two solutions.
The equation has a unique solution. This solution is a noninteger rational number.
The solution is \(x = 0\).
The equation has a unique solution. This solution is a positive integer.
The equation has a unique solution. This solution is a negative integer.