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Algebra II

Log of many Logs
How can I compute the values of $n$ for which the following expression exists?
$\log_{e} (\log_{e} (\log_{e} (\log_{e} (\dots \log_{e} (n))))$
It is for instance apparent that when $n = e$ , the second application of $\log_{e}$ is undefined.

mriteyl 2022-09-01

How to solve a system of logarithmic equations?
I need to create a function with the following properties:
$f (1) = 1$
$f (65) = 75$
$f (100) = 100$
Additionally, the function needs to grow logarithmically. So that gives three equations:
$A \cdot \ln (B \cdot 1 + C) = 1$
$A \cdot \ln (B \cdot 65 + C) = 75$
$A \cdot \ln (B \cdot 100 + C) = 100$
I am having trouble with using substitution to solve this. Barring there is no analytic way to solve this system, how would I use a numerical approximation for $A, B$ and $C$ ?

opinaj 2022-09-01

Determine which of the following differential equations are separable. Do not solve the equations. $y^{'} = \ln (x y)$

cvnoticiasdg 2022-08-31

If y varies inversely with x and y = 3 when x = 4, what is the value of y when x = 2?

ngombangouh 2022-08-31

During one day of trading in the stock market, and investor lost $2500 on one stock, but gained $1700 on another. At the end of trading that day, the investor's holdings in those tow stocks were worth $52,400. What were they worth when the market opened that day?

mastegotgd 2022-08-31

Is y=2x an inverse variation?

Corinne Woods 2022-08-31

The cables of a suspension bridge are in the shape of a parabola. The towers supporting the cables are 600feet apart and 80 feet high. If the cables touch the road surface midway between the towers, what is the height of the cable at a point of 150 feet from the center of the bridge?

Eisregiony1 2022-08-31

The health care provider is preparing to administer "insulin glargine" (Lantus), a long-acting insulin drug. The doctor orders 40 units to be given SC at 0900. Your supply is "insulin glargine" 100 units / ml. How many mL will be administered?

fermetrakr 2022-08-31

If the discriminant is positive, but not a perfect square, the quadratic equation will have two different rational roots.
true of false

Asher Kaufman 2022-08-31

How do you write an inverse variation equation that relates x and y when you assume that y varies inversely as x given that if y=124 when x=12, find y when x= -24?

ignizeddyug 2022-08-31

Integral $\int_{0}^{1} \sqrt{\frac{\ln x}{x^{2} - 1}} d x$
Please help evaluating this integral
Mathematica could not evaluate it in a closed form. Numerically it is about
$I \approx 1.060837861412045137097...,$

saborcehj 2022-08-31

For what value(s) of x is it true that $(\log X)^{3} = 3 \log X$ ?

nascarchic839e9 2022-08-31

Find the solution:
$2 x + 1 - 3 x = 6 x = ?$

Brynn Collins 2022-08-31

When 80%of a number to the number, the result is 252. what is the number?

Cyrus Munoz 2022-08-31

What is the solution for the equation 3x + 6 = 12?

Kubaczynjo 2022-08-31

How is $\arctan (\sinh (x * π))$ the inverse of $\log (\tan (x)) / π$
How is
$\arctan (\sinh (x * π))$
the inverse of
$\frac{\log (\tan (x))}{π}$
What is the relationship between $\log (x)$ and $\sinh (x)$ . I guess is what my real question is.

ximblajy 2022-08-31

How do I calculate the inverse function of this function?
I have this function:
$f (x) = \frac{1 + \ln (x)}{1 - \ln (x)}$
And i should calculate $f^{- 1} (x)$
I am not really sure how to proceed but I think that the first step would be to have x alone, how do I achieve that?

hetjurnar02 2022-08-31

inverse of quadratic log functions
Can a Log function with a quadratic have an inverse function? The specific question is to find the inverse of
$f (x) = \log_{2} (x^{2} - 3 x - 4)$
The function already fails the horizontal line test, but apparently there is a function of
If
$x > 4, f^{- 1} (x) = \frac{3 + \sqrt{2^{x + 2} + 25}}{2}$
If
$x < - 1, f^{- 1} (x) = \frac{3 - \sqrt{2^{x + 2} + 25}}{2}$
I was able to find this by swapping the x and y around, but why does it have an inverse function?

Asher Kaufman 2022-08-31

Any power of logarithm is $O (N)$
This is more of a computer science question but it uses calculus and proof techniques so I think it might be more appropriate here. Basically, how do I prove that,
for any constant $K \geq 1$ , that $\log^{K} (N) = O (N)$
Where O denotes the Big O.I am thinking of proving this by induction but not sure what the base case should. In addition to this, I think L'Hopital's rule can be used here with the two functions. Can anyone give me a solid hint on how to start this ? Many thanks !

Loldi9s 2022-08-31

Simplyfing Log Question
Don't know the concepts of diving and multiplying whole logs.
$\frac{\log_{a} (x)}{\log_{a} (y)} \cdot \frac{\log_{b} (y)}{\log_{b} (x)}$
Can you please tell me how to simplify this?

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