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
kogti [31]
3 years ago
15

Logx - logx-1^2=2log(x-1)

Mathematics
2 answers:
myrzilka [38]3 years ago
8 0

Answer:

x is approximately 2.220744

Step-by-step explanation:

This can be simplified a little using properties of logarithms, and then solve it by graphing:

log(x)-log(x-1)^2=2\,log(x-1)\\log(x)-2\,log(x-1)=2\,log(x-1)\\log(x)=4\,log(x-1)

So we use a graphing tool to find the intersection point of the graph of log(x), and the graph of 4\,log(x-1)

Please see attached image for the graph and solution.

The value of x is approximately 2.220744

Airida [17]3 years ago
8 0

Answer:

  x = 2.32011574011

Step-by-step explanation:

The problem with your original equation is that it is a long way of saying ...

  log(x) -log(x) -1 = 2log(x-1)

  0 -1 = 2log(x-1)

which has the solution ...

  -1/2 = log(x -1)

  1/√10 = x -1

  x = 1 + 1/√10 ≈ 1.3162278

__

We have asked for clarification, and what we got was ...

  \log{(x)}-\log{(x-1^2)}=2\log{(x-1)}

which, again, is a long way of saying ...

  \log{(x)}-\log{(x-1)}=2\log{(x-1)}

The other reasonable interpretation of your 'clarified' equation is ...

  \log{(x)}-\log{((x-1)^2)}=2\log{(x-1)}

which you already have an answer to. You have declared that a "misconception."

So, we are left with the interpretation that the equation you want a solution to is ...

  \log{(x)}-\log{(x-1)}=2\log{(x-1)}

_____

When solving these graphically, I like to write the equation as a function whose zero(s) we're trying to find. For this, when we subtract the right side, we get ...

  f(x)=\log{(x)}-3\log{(x-1)}

A graphing calculator shows that f(x) = 0 when ...

  x ≈ 2.32011574011

__

If you don't like my interpretation, check out the second attachment. It has your x-1² as the argument of the middle term. You can see that the calculator interpreted that the same way I did (as required by the order of operations).

You might be interested in
In the diagram, polygon ABCD is flipped over a line of reflection to make a polygon with vertices at A′, B′, C′, and D′. Points
DIA [1.3K]
<span>if point A( 2,2) is reflected across the line Y then the new position A' is (-2,2) and the distance AY = distance A'Y if A is reflected across line R it is now at point B and the distance AR = distance BR lets say the point A(2,2) was perpendicular to the line R at the point (1, 4) then when reflected the point A now at location B will have coordinates</span><span>when flipped over a line of reflection the lengths are still the same the point to the line of reflection is the same length as the line of reflection to the reflected position the distance from the original point to the reflected point is twice the distance from the original point to the line of reflection cannot see your polygon. here is an example

</span>

7 0
3 years ago
Are the leap years divisible by 2​
Helen [10]
Any year that is evenly divisible by 4 is a leap year.
8 0
3 years ago
Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box cos
n200080 [17]
The answer would be 15 boxes!
4 0
3 years ago
Read 2 more answers
PLEASE HELP 99 POINTS!!!
TEA [102]
Here, Angles under a straight line would be equal to 180
So, 70 + 60 + y = 180
130 + y = 180
y = 180 - 130
y = 50

Now, x = y  [ As they are vertically opposite angles ]

In short, Your Answer would be 50

Hope this helps!
5 0
3 years ago
Read 2 more answers
You have the same bowl, with 5 orange, 6 blue, 3 green, 4 red and 7 yellow candies. You take out an orange candy
xeze [42]
Answer: B) 1/6

Explanation: First, we want to add up all the candies, and after doing that we discover that there are 25 candies in total. Next, we take away an orange candy, leaving us with 4 orange candies, but it also takes away 1 from the number of total candies, leaving us with 24 total candies. Finally, we put orange candies as our numerator and total candies as our denominator and get 4/24, which simplified becomes 1/6.
5 0
3 years ago
Read 2 more answers
Other questions:
  • When you divide 4 by 7 the quotient is a
    6·2 answers
  • Please please help if you can it would mean a lot. Thank you!!
    15·1 answer
  • The shortest side of a triangle is 9 greater than twice the shortest side of a similar triangle. If the ratio of similitude is 7
    7·1 answer
  • What is the simplified form of square root of 45
    15·2 answers
  • What is the solution to the expression Negative 2 minus 3 minus (negative 4)?
    12·2 answers
  • Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1? On a coordinate plane, a vertical dashed line at (n
    8·2 answers
  • Paul is saving for a down payment to buy a house. The account earns 13% interest compound quarterly, and he wants to have $15,00
    6·1 answer
  • It has been decided that 100 people need to be surveyed to decide the publics opinion on a school building project. A student su
    7·1 answer
  • Can someone help with 7-11 please ?
    9·1 answer
  • A government agency reports that 22% of baby boys 6-8 months old in the United States weigh less than 25 pounds. A sample of 147
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!