Question

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.)

Answer 1

Answer:

$-\frac{ln(662)-2}{4}$

{-1.12}

Step-by-step explanation:

$e^{2 - 4x} = 662$

Solve this exponential equation using natural log

Take 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 approximation

x=-1.12381x=-1.12