Find All the Real-Number Roots of the Equation $\log _ { 7 } x + \log _ { 7 } ( x + 9 ) = 0$

question 6

Multiple Choice

Find all the real-number roots of the equation. Give an exact expression for the root and also(where appropriate) a calculator approximation rounded to three decimal places. $\log _ { 7 } x + \log _ { 7 } ( x + 9 ) = 0$

• A) \(x = \frac { - 9 + \sqrt { 85 } } { 2 } \approx 0.110\)
• B) \(x = \frac { - 9 - \sqrt { 85 } } { 2 } \approx - 9.110\)
• C) \(x = \frac { 9 - \sqrt { 85 } } { 2 } \approx - 0.253\)
• D) \(x = \frac { 9 + \sqrt { 85 } } { 2 } \approx 0.253\)
• E) no solution