Solve the Equation $$e ^ { 7 x } = - 9 e ^ { 2 x }$$

question 42

Multiple Choice

Solve the equation. Write the solution set with the exact values given in terms of natural or common
logarithms. Also give approximate solutions to 4 decimal places, if necessary.
- $$e ^ { 7 x } = - 9 e ^ { 2 x }$$

• A) \(\left\{ \frac { \ln 9 } { 5 } \right\} ; x \approx 2.2756\)
• B) \(\left\{ \frac { \ln - 9 } { 5 } \right\} ; x \approx 2.2756\)
• C) \(\left\{ \frac { \ln 9 } { - 5 } \right\} ; x \approx - 2.2756\)
• D) \{ \}

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Definitions:

Degrees of Freedom

The quantity of distinct variables or measures that may fluctuate during an evaluation without breaching any restrictions.

Test Statistic

A calculated value used to determine whether to reject the null hypothesis in statistical hypothesis testing.

Critical Value

A point on the scale of a test statistic beyond which we reject the null hypothesis; it depends on the chosen significance level.

Test Statistic

A value calculated from sample data during a hypothesis test.