Solve the Exponential Equation $$4 ^ { x + 4 } = 5 ^ { 2 x + 5 }$$

question 17

Multiple Choice

Solve the exponential equation. Express the solution set in terms of natural logarithms.
- $$4 ^ { x + 4 } = 5 ^ { 2 x + 5 }$$

• A) \(\left\{ \frac { 5 \ln 5 - 4 \ln 4 } { \ln 4 - 2 \ln 5 } \right\}\)
• B) \(\left\{ \ln \left[ \frac { 5 ^ { 5 } } { 4 ^ { 4 } } - \frac { 4 } { 5 ^ { 2 } } \right] \right\}\)
• C) \(\{ \ln 5 - \ln 4 \}\)
• D) \(\{ 7 \ln 5 - 5 \ln 4\) Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.

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