1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
viva [34]
3 years ago
9

Ln(1/e^2) without calculator

Mathematics
2 answers:
castortr0y [4]3 years ago
7 0
Once you remember the definition of a log, the answer to this question will literally fall out of your pencil.

First, ' Ln ' means 'natural log' ... logs to the base of ' e '.

Definition of the natural log of a number:
In order to get the number, what power do I have to raise ' e ' to ?

OK.  What power do you have to raise ' e ' to in order to get  1/e²  ?

Isn't  1/e²  the same thing as  e⁻²  ?

So, in order to get  1/e² , you have to raise ' e ' to the  -2  power .

In math-speak:    Ln(1/e²) = <em><u>-2</u></em> .
AlladinOne [14]3 years ago
5 0
Ln 1/e²
             =  Ln 1 -  Ln e²       as  Ln X/Y = Ln X  -  Ln Y
             =  0  -  2 Ln e         as Ln 1 = 0    and  Ln X²  = 2 Ln X
                = - 2  * 1          as Ln e  = 1

        = -2


You might be interested in
A circle has a 10 centimeter radius. Find the area of the circle to the nearest tenth. (Use 3.14 for ?)
pickupchik [31]

Answer:

314.2 cm^2

Step-by-step explanation:

The formula for the area of a circle of radius r is A = 3.14r^2.

With r = 10 cm, r^2 = 100 cm^2, and so the area of this circle is 314.2 cm^2, to the nearest tenth.

3 0
3 years ago
Question 1 of 10 Diana invested $3000 in a savings account for 3 years. She earned $450 in interest over that time period. What
dangina [55]

Hey there!!

The question states that a sum is invested which is $3000 and hence, this would be counted as the principle amount or the principle sum.

The term given is 3 years, which gives us the idea that this interest is being counted or being active for 3 years.

She ( Diana ) earned the sum $450 at the end of three years. This means, the simple interest is $450.

Never get confused with the principle amount, principle sum and interest.

<u><em>Principle amount = Principle sum + The interest. </em></u>

Formula given :

I = prt

'p' is denoted as the principle sum, r is the rate and the t is the term or the number of years.

Now, plugging in all the values :

... <em>450 = 3000×r×3 </em>

... <em>450 = 9000×r </em>

... <em>r = 450 / 9000</em>

... <em>r = 0.05 </em>

... <em>r = 5% </em>

As we need the answer in the decimal form, the answer would be <em><u>0.05</u></em>

Hope my answer helps!!<em> </em>

4 0
3 years ago
What is the degree of t-4t^2+2t^3
Ierofanga [76]

Answer:

3

Step-by-step explanation:

t-4t^2+2t^3

Rewriting this in order from largest to smallest exponent

2t^3 -4t^2 +t

The highest power is 3

So this is degree 3

4 0
3 years ago
I need help which answer choice is it
Tatiana [17]
The answer is (9/2)/(3/2), the answer choice in the bottom right corner.
8 0
3 years ago
Jack has $37 and saves $6.50 per week. Diane has $9 and saves $8.25 per week. Define a variable, then write and solve an equatio
otez555 [7]

Answer:

Defining variable: x = per week

Equation: 37 + 6.5x = 9 + 8.25x

Answer: 16 weeks

Step-by-step explanation:

x = per week

Jack:

37 + 6.5x

Diane:

9 + 8.25x

Equation:

37 + 6.5x = 9 + 8.25x

6.5x - 8.25x = 9 - 37

-1.75x = -28

x = 16

3 0
3 years ago
Other questions:
  • Which of the following is a polynomial with roots 2, 3i, and −3i? f(x) = x3 − 2x2 + 6x − 9 f(x) = x3 − 6x2 + 9x − 18 f(x) = x3 −
    8·2 answers
  • The distance from Jim's house to the intersection of Thornwood Drive and Holly Drive is given by the expression 15x − 7. The tot
    7·2 answers
  • Explain prime factorization of 2025
    8·1 answer
  • Which ordered pair is the best estimate for the
    15·1 answer
  • Write down a pair of integers whose
    10·1 answer
  • (y+3) (y^2-3y+9) What is the product? y3 + 27 y3 – 27 y3 – 6y2 + 27 y3 + 6y2 + 27
    10·2 answers
  • Find all real zeros of the function. <br>5. f(x) = x3 - 3x2 - 6x + 8 <br>6. g(x) = x3 + 4x2 - x - 4​
    9·2 answers
  • A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)e^kt, where m(0) is the initial mass and k is a n
    12·1 answer
  • When they arrived in Philadelphia, Tyler’s family took a taxi to a museum. The taxi charged $2.70 per mile, and they paid the dr
    9·1 answer
  • 5 x 4\9 can you tell me the way to get the answer
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!