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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.)

Respuesta :

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 log

Take 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 approximation

x=-1.12381x=-1.12