MATH SOLVE

3 months ago

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