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Tomtit [17]
3 years ago
10

Expanding Logarithmic Expressions In Exercise, use the properties of logarithms to rewrite the expression as a sum, difference,

or multiple of logarithms.
In (x^2 - 1)^1/3
Mathematics
1 answer:
Leya [2.2K]3 years ago
5 0

Answer:  \dfrac{1}{3}[\ln (x+1)+\ln(x-1)]

Step-by-step explanation:

Properties of logarithm :

  1. \log (ab)= \log a+\log b
  2. \log(\dfrac{a}{b})=\log a-\log b
  3. \log a^n= n\log a

The given expression in terms of Natural log : \ln (x^2 - 1)^{\frac{1}{3}}

This will become \dfrac{1}{3}\ln (x^2 - 1)      [ By using Property (3)]

=\dfrac{1}{3}\ln (x^2-1^2)

=\dfrac{1}{3}\ln ((x+1)(x-1))   [\because a^2-b^2=(a+b)(a-b)]

=\dfrac{1}{3}[\ln (x+1)+\ln(x-1)]   [ By using Property (1)]

Hence, the simplified expression becomes \dfrac{1}{3}[\ln (x+1)+\ln(x-1)] .

You might be interested in
A thermos in the shape of a cylinder is filled with coffee. The height of the cylinder is 12 inches and its radius is 2 inches.
serg [7]

Answer:

The  volume of coffee in the thermos is 150.72 inches³ .

Step-by-step explanation:

Formula

Volume\ of\ a\ cylinder = \pi r^{2}\ h

Where r is the radius and h is the height .

As given

A thermos in the shape of a cylinder is filled with coffee.

The height of the cylinder is 12 inches and its radius is 2 inches.

As

\pi = 3.14

Put all the value in the formula

Volume\ of\ a\ cylinder = 3.14\times 2\times 2\times 12

                                              =  150 .72 inches ³

Therefore the volume of coffee in the thermos is  150 .72 inches ³ .

3 0
3 years ago
I don't understand this question 5,925,020 = 5,000,000 + ------ + 20,000 ----- + 2O
miv72 [106K]

5925020 = 5000000+<u>900000</u>+20000+<u>5000</u>+20

Hope it helps. Please do comment

5 0
3 years ago
Gina Needs To Pack 130 Pens, 50 Pencils And 20 Erasers Into Identical Gift Bags So That Each Item Is Equally Distributed Among T
PolarNik [594]

Answer:

Step-by-step explanation:

I think the best way is to split up the erasers before you do anything. That would mean there were 20 gift bags in all

If you did that, then each gift bag would contain 2 pencils with 10 left over.

Further 130 pens would divide up into 6 pens in each gift bag with 10 pens left over.

6 0
3 years ago
HELP please.
Scorpion4ik [409]

Answer:

C

Step-by-step explanation:

Here, originally, we are told that the point Q has coordinates (-2,1)

Now, its dilated point has the coordinates (-8,4)

what we can observe here is the the shape original polygon was dilated by a factor of 4 to give the image

Now the point R’ is (0,8)

To get the point R , we simply divide each coordinate by 4

Thus, we have (0/4 , 8/4)

This is same as option C

4 0
3 years ago
What is the area of this figure?
Alborosie

Answer:

146

Step-by-step explanation:

Hey there to find the area of this shape we will divide it into 2 shapes first one is a trapezoid and the second one is a triangle. first, we find the area of a trapezoid. to find the area of a trapezoid we use the formula:

        A = \frac{a+b}{2} * h          

in this situation

a = 4

b = 14

h = 10

Now we plug it into the formula which will look like:

       A = \frac{4+14}{2}*10

if we solve it:

4+14 = 18

18/2 = 9

9*10 = 90

so the area of the trapezoid is 90

Now we find the area of triangle. to find the area of a triangle we use the formula:

   A = \frac{1}{2} * b * h

in this situation

b = 14

h = 8 ( because the height of the trapezoid was 10 and the height of both shapes combined is 18 so we do 18 - 10 = 8 )

Now we put the numbers into the formula  which will look like:

    A = \frac{1}{2}*14*8

if we solve it :

14*8 = 112

112*\frac{1}{2} = 56

so the area of the triangle is 56

Now we add the area of both shapes:

56 + 90 = 146

area of the big shape = 146

Have a wonderful day

7 0
3 years ago
Read 2 more answers
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