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Ne4ueva [31]
3 years ago
12

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.)
Mathematics
1 answer:
Cloud [144]3 years ago
7 0

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

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