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
ExtremeBDS [4]
3 years ago
10

Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or m

ultipal of logarithms.See example 3.
In 2x/(x^2 - 1)1/2
Mathematics
1 answer:
wel3 years ago
6 0

Answer:

\frac{1}{2}ln(2x)-\frac{1}{2}ln(x^2-1)

Step-by-step explanation:

In 2x/(x^2 - 1)1/2

ln(\frac{2x}{x^2-1} )^\frac{1}{2}

Apply the property of natural log

ln x^m = m ln(x) move the exponent before ln

ln(\frac{2x}{x^2-1} )^\frac{1}{2}

\frac{1}{2}ln(\frac{2x}{x^2-1})

ln(m/n)= ln m - ln n

\frac{1}{2}(ln(2x)-ln(x^2-1))

multiply 1/2 inside the terms

\frac{1}{2}ln(2x)-\frac{1}{2}ln(x^2-1)

You might be interested in
Write each rational number in the form a/b, where a and be are integers
gizmo_the_mogwai [7]
I have no clue sorry
7 0
3 years ago
When graphing y = 2x2 + 35x + 75, which viewing window would allow you to see all of the intercepts and the minimum as closely a
djverab [1.8K]

The intercept with the y-axes occurs when x = 0

f(0) = 2*02 + 35*0 + 75 = 0 + 0 + 75 = 75

So intercept with x axes is the point (0,75)

The intercept with the x-axes occurs when y=0

2x2 + 35x + 75 = 0

<span>As there’s no direct way to find x, we can use the <span>Bhaskara formula:</span></span>

x=(-b+- square root (b2-4ac))/(2a)

This formula is for: ax2 +bx + c = 0

So:

a=2

b=35

c=75

x=(-35+- square root (35^2-4*2*75))/(2*2)

So x can be -2.5 or -15

So intercept with y axes are the points (-2.5,0) and (-15,0)

And there is also a formula to find the mínimum. The mínimum is always the vertex:

Xv = -b/(2*a) = -35/(2*2) = -8.75

Yv = f(Xv) = f(-8.75) = 2(-8.75)^2 + 35(-8.75) <span> + 75 = </span>-78.125

So the minimum is the point (-8.75, -78.125)

You can easily verify all these data with a graphic software such as GeoGebra.

Here is the complete list of all the points we need to see:

(0,75); (-2.5,0) ; (-15,0), (-8.75, -78.125)

So the mínimum X has to be -15 and the máximum X has to be 0

and the mínimum Y has to be -78.125 and the máximum Y has to be 75

So this leads to a different scale for X and for Y.


Window x = [ -15, 0] y = [ -78.125, 75]
5 0
3 years ago
Find the value of x in the isosceles triangle shown below.
Reptile [31]

Answer:

x=10

Step-by-step explanation:

We can use the Pythagorean theorem to find x

The height meets the base at a right angle

The base is bisected ( cut in half) so the base is 6 the height is 8

a^2 + b^2 = c^2

6^2 + 8^2 = x^2

36+64 = x^2

100 = x^2

Taking the square root of each side

sqrt(100) = sqrt(x^2)

10 = x

4 0
3 years ago
Read 2 more answers
The quotient of any two integers is an intiger? True or false
Serggg [28]
The correct answer is true since an integer is simply just a number
4 0
3 years ago
The relation described in this statement can be classified as which of the following? The total distance traveled and the time s
Rzqust [24]
<span>The relation described in this statement can be classified as </span><span>both a relation and a function. </span>
7 0
3 years ago
Other questions:
  • A gardener is drawing plans for a new yard. She creates the picture below to represent the size and shape of a new lawn. How can
    9·2 answers
  • A system of linear equations is shown below. 2x + 4y = 10 3x – y = 8 marla is attempting to prove that by replacing 2x + 4y = 10
    14·1 answer
  • I need help dont know how to do this.
    12·1 answer
  • the ratio of numbers who wear glasses to the total class is 2:5 what is the ratio of students who wear glasses to those who don'
    11·1 answer
  • Geometry math question no Guessing and Please show work
    12·1 answer
  • David drops a ball from the top of a building with a height of 64 feet.
    13·1 answer
  • Do i add 40 + 45? Or multiply
    9·1 answer
  • Help me and I’ll give brainliest to u
    6·1 answer
  • 7.
    9·1 answer
  • Find the maximum value on (0, infinity) for f(x)=7x-2xlnx
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!