Solve the Equation $$\left( \frac { 1 } { 2 } \right) ^ { x } = 7 ^ { 1 - x }$$

question 320

Multiple Choice

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places.
- $$\left( \frac { 1 } { 2 } \right) ^ { x } = 7 ^ { 1 - x }$$

• A) \(\frac { \ln \left( \frac { 1 } { 2 } \right) + \ln 7 } { \ln 7 } \approx 0.644\)
• В) \(\frac { \ln 7 } { \ln \left( \frac { 1 } { 2 } \right) + \ln 7 } \approx 1.553\)
• C) \(\ln \left( \frac { 1 } { 2 } \right) - \ln 7 \approx - 2.639\)
• D) \(\frac { \ln 14 } { \ln 28 } \approx 0.792\)