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3 years ago

9

Ln(1/e^2) without calculator

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

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Please help me with this!

ivanzaharov [21]

1. The first equation is - 2x + 5y = 0

Second equation is $y = \frac{2}{5} x$

5y = 2x

- 2x + 5y = 0

Hence, the two equations are equivalent.

2. $a_{1} = 2, a_{2} = - 2$

$b_{1} = -1, b_{2} = -1$

$\frac{a_{1} }{a_{2}} =\frac{2}{-2} = -1$

$\frac{b_{1} }{b_{2}} = \frac{-1}{-1} = 1$

$\frac{a_{1} }{a_{2}} \neq \frac{b_{1} }{b_{2}}$

Hence, the equations are consistent.

3. $a_{1} = 4, a_{2} = 6$

$b_{1} = -1, b_{2} = -1$

$\frac{a_{1} }{a_{2}} =\frac{4}{6} = \frac{2 }{3}$

$\frac{b_{1} }{b_{2}} = \frac{-1}{-1} = 1$

$\frac{a_{1} }{a_{2}} \neq \frac{b_{1} }{b_{2}}$

Hence, the equations are consistent.

4. Equations can be re-arranged as:

x + y - 4 = 0 and

x + y + 6 = 0

$a_{1} = 1, a_{2} = 1$

$b_{1} = 1, b_{2} = 1$

$c_{1} = -4, c_{2} = 6$

$\frac{a_{1} }{a_{2}} =\frac{1}{1} = 1$

$\frac{b_{1} }{b_{2}} =\frac{1}{1} = 1$

$\frac{c_{1} }{c_{2}} =\frac{-4}{6} = \frac{-2}{3}$

$\frac{a_{1} }{a_{2}} = \frac{b_{1} }{b_{2}} \neq \frac{c_{1} }{c_{2}}$

Hence, the equations are inconsistent.

5. If we multiply the first equation by 4, we will get,

2y = -4x + 20 which is the second equation.

Hence, the equations are equivalent.

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3 years ago

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mihalych1998 [28]

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3 years ago

Please solve asap thanks

tensa zangetsu [6.8K]

I think..

A' =( -1,-4 )

B' = ( 3,-2 )

C'=( - 2, 2 )

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ryzh [129]

Answer:

Step-by-step explanation:

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