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elena-s [515]
2 years ago
6

Use natural logarithms to solve the equation. e2x = 1.4 Round to the nearest thousandth.

Mathematics
2 answers:
Firlakuza [10]2 years ago
5 0

Answer: x=0.168

Step-by-step explanation:

To solve the equation e^{2x}=1.4 you need to apply natural logarithm to both sides of the equation:

ln(e)^{2x}=ln(1.4)

According to the logarithms property:

ln(b)^a=aln(b)

Then, applying the property, you get:

(2x)ln(e)=ln(1.4)

You need to remember the following:

ln(e)=1

Therefore:

2x(1)=ln(1.4)\\\\2x=ln(1.4)

And finally, you must divide both sides of the equation by 2:

\frac{2x}{2}=\frac{ln(1.4)}{2}\\\\x=0.1682

Rounded to the nearest thousand:

x=0.168

harina [27]2 years ago
4 0

Answer:

x = 0.16823611831

Step-by-step explanation:

ln (natural log), when multiplied by e, cancels it out.

Therefore ln*e2x = ln*1.4

2x = 0.33647223662

x = 0.16823611831

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Which of the following illustrates the truth value of the given conditional statement?
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Answer:

~p -> ~q

Step-by-step explanation:

A conditional statement in logic may be symbolized by the alphabets, p and q, It always contains an if - then statement.

There is always a  logical connector in the statement with the symbol ->.

A conditional statement is false if the hypothesis is true and the conclusion is false.

The statement in the answer above reads in word; "if not p then not q".

6 0
3 years ago
Simplify &gt;&gt;&gt;&gt;&gt;&gt;&gt; <br><br><br> 2(4x+9)
Black_prince [1.1K]

2(4x+9)

mutiply the bracket by 2

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8 0
3 years ago
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nika2105 [10]

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Step-by-step explanation:

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3 years ago
A positive integer is twice another.the sum of the reciprocal of the two positive integer is 3/14. Find the integers
icang [17]

Answer:

\huge\boxed{14\ \text{and}\ 7}

Step-by-step explanation:

n,\ m-\text{positive integer}\\\\n=2m-\text{a positive integer is twice another}\\\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}-\text{the sum of the reciprocal of the two positive integer is }\ \dfrac{3}{14}\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}n=2m&(1)\\\dfrac{1}{n}+\dfrac{1}{m}=\dfrac{3}{14}&(2)\end{array}\right

\text{Substitute (1) to (2):}\\\\\dfrac{1}{2m}+\dfrac{1}{m}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{1\cdot2}{m\cdot2}=\dfrac{3}{14}\\\\\dfrac{1}{2m}+\dfrac{2}{2m}=\dfrac{3}{14}\\\\\dfrac{1+2}{2m}=\dfrac{3}{14}\\\\\dfrac{3}{2m}=\dfrac{3}{14}\Rightarrow2m=14\qquad\text{divide both sides by 2}\\\\\dfrac{2m}{2}=\dfrac{14}{2}\\\\\boxed{m=7}

\text{Substitute it to (1):}\\\\n=2\cdot7\\\\\boxed{n=14}

8 0
2 years ago
In the right triangle above a=2.7 and b=4.3. Find the value of c, rounded to the nearest tenth
morpeh [17]

Answer:

  5.1

Step-by-step explanation:

Since there is no diagram provided here, we assume that c is the length of the hypotenuse, so we have ...

  c² = a² +b² . . . . . . Pythagorean theorem

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  c ≈ 5.1

7 0
3 years ago
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