Q:

# Solve the following exponential equation by taking the natural logarithm on both sides. Express the solution in terms of natural logarithms Then. use a calculate obtain a decimal approximation for the solution. e^2 - 4x = 662 What is the solution in terms of natural logarithms? The solution set is { }. (Use a comma to separate answers as needed. Simplify your answer Use integers or fractions for any numbers in expression). What is the decimal approximation for the solution? The solution set is { }. (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Accepted Solution

A:
Answer: $$-\frac{ln(662)-2}{4}$${-1.12}Step-by-step explanation:$$e^{2 - 4x} = 662$$Solve this exponential equation using natural logTake natural log ln on both sides$$ln(e^{2 - 4x}) = ln(662)$$As per the property of natural log , move the exponent before log$$2-4x(ln e) = ln(662)$$we know that ln e = 1$$2-4x= ln(662)$$Now subtract 2 from both sides$$-4x= ln(662)-2$$Divide both sides by -4$$x=-\frac{ln(662)-2}{4}$$Solution set is {$$x=-\frac{ln(662)-2}{4}$$}USe calculator to find decimal approximationx=-1.12381x=-1.12