Try to relax. Your desperation has surely progressed to the point where
you're unable to think clearly, and to agonize over it any further would only
cause you more pain and frustration.
I've never seen this kind of problem before. But I arrived here in a calm state,
having just finished my dinner and spent a few minutes rubbing my dogs, and
I believe I've been able to crack the case.
Consider this: (2)^a negative power = (1/2)^the same power but positive.
So:
Whatever power (2) must be raised to, in order to reach some number 'N',
the same number 'N' can be reached by raising (1/2) to the same power
but negative.
What I just said in that paragraph was: log₂ of(N) = <em>- </em>log(base 1/2) of (N) .
I think that's the big breakthrough here.
The rest is just turning the crank.
Now let's look at the problem:
log₂(x-1) + log(base 1/2) (x-2) = log₂(x)
Subtract log₂(x) from each side:
log₂(x-1) - log₂(x) + log(base 1/2) (x-2) = 0
Subtract log(base 1/2) (x-2) from each side:
log₂(x-1) - log₂(x) = - log(base 1/2) (x-2) Notice the negative on the right.
The left side is the same as log₂[ (x-1)/x ]
==> The right side is the same as +log₂(x-2)
Now you have: log₂[ (x-1)/x ] = +log₂(x-2)
And that ugly [ log to the base of 1/2 ] is gone.
Take the antilog of each side:
(x-1)/x = x-2
Multiply each side by 'x' : x - 1 = x² - 2x
Subtract (x-1) from each side:
x² - 2x - (x-1) = 0
x² - 3x + 1 = 0
Using the quadratic equation, the solutions to that are
x = 2.618
and
x = 0.382 .
I think you have to say that <em>x=2.618</em> is the solution to the original
log problem, and 0.382 has to be discarded, because there's an
(x-2) in the original problem, and (0.382 - 2) is negative, and
there's no such thing as the log of a negative number.
There,now. Doesn't that feel better.
The reason for one graph appears skewed, and one graph appears symmetric is the interval on the x-axis of the histogram is inconsistent.
<h3>What is histogram?</h3>
A histogram is the way of representation of data which is used to show the frequency distribution using the rectangle similar to a bar graph.
In the problem, the data given as,
- In the attached image below, the histogram and box plot is shown for the ages of Elizabeth's Grandchildren and their frequency.
- In the 3rd and 4the bar of histogram, the data is jumped from 14 to 20 instead of 15.
- The frequency distribution in histogram for this data is inconsistent.
- This inconsistency brought the between the two graphs.
Thus, the reason of one graph appears skewed, and one graph appears symmetric is the interval on the x-axis of the histogram is inconsistent.
Learn more about the histogram here;
brainly.com/question/2962546
Solution:
- Perimeter of Rectangle = 346
Let Required length of breadth be x
- Then, Length of Rectangle = 45 + x
Now, We have ;
- Perimeter of Rectangle = 2(l+b)
- Perimeter of Rectangle = 2 ( 45 + x + x
- 346 = 2 ( 45 + 2x )
- 346 = 90 + 4x
- 346 - 90 = 4x
- 256 = 4x
- x = 256 ÷ 4
- x = 64 inches
So, Length of Rectangle = x + 46
Length of Rectangle = 64 + 46
Length of Rectangle = 110 inches
Now, Breadth of Rectangle = 64 inches.
