0
votes
2answers
22 views

Find the inverse of the function

Find the inverse of the function $f(x) = -2 \cdot4^{2(x-3)} - 1$.
0
votes
0answers
23 views

Function inverse mapping [0, +inf) to [0, 1)

I have a measure ($x$) which the domain is $[0, +\infty)$ and measure some sort of variability. I want to create a new measure ($y$) that represents regularity and is inverse related to $x$. It is ...
0
votes
1answer
29 views

Prove this logarithm equation

I keep getting the wrong answer. Can someone please correct my working out a^x=b^(1-x) In(a)^x=In(b)^(1-x) xIn(a)=(1-x)In(b) xIn(a)=In(e)-xIn(b) xIn(a)+xIn(b)=In(e) x[In(a)+In(b)]=Ine ...
0
votes
1answer
39 views

Inverse Function of Logarithm

The answer is A but I don't understand why! $ -2 \log_e (x^2) $ can be re-written as $ -4 \log_e(x) $ right? but why do these two graphs look different? the graph $-2 \log_e (x^2) $ is one to ...
0
votes
1answer
15 views

Maximum value of constant in logarithm problem

The first thing I did was: make: (x-1)^2 - k > 0 (x-1)^2 > k don't know what to do after this point... the maximum value of k is 9 i dont really understand what the maximum value of k is? ...
0
votes
1answer
60 views

Graphing: Given two points on a graph, find the logarithmic function that passes through both.

Is there such a method to do this? I would like to come up with a logarithmic function (a graph that looks like a square root graph) that passes through two given points. Haven't had any luck in ...
0
votes
0answers
33 views

Scaling a big range of small numbers to a small range of big numbers

I'm trying to make a volume meter in a Flash program. I have data coming in like: 0.008 0.0005 0.1 0.02 These numbers indicate the volume of a sound coming in ...
0
votes
2answers
66 views

Find Log equation from data points

I have the following data points, (left hand column goes from 0-127, right hand column goes from 30-22000 hz. Is there any calculator I can use to find a "log" function of this data, so that it comes ...
0
votes
1answer
19 views

Steps to Graph Exponential Equations & Absolute Value

how to sketch: $-e^{|-x-1|} + 2$ Can someone clarify: $|f(x)|:$ we draw $f(x)$ and then reflect the ($-y$ parts) in the $x$-axis $f|(x)|:$ we draw $f(x)$ and then reflect the ($-x$ parts) in the ...
1
vote
1answer
28 views

Show that $g(x)=x\ln{x}$ and $g(x)=e^x$ are bounded below.

Show that $g(x)$ is bounded below, for $0\leq x$: a) $g(x) = \left\{ \begin{array}{ll} 0 & \mbox{if } x=0 \\ x\ln{x} & \mbox{if } x>0 \end{array} \right.$ b) $g(x)=e^x$ For (a), ...
0
votes
1answer
14 views

Creating a constrained log function

Good morning, I have a series of values that I intend to use as the exponents and I would like to create a log function so that: $Log_x(y_1)=.1$ $Log_x(y_2)=.2$ $Log_x(y_3)=.3$ ... ...
0
votes
1answer
40 views

Give the domain and range of $y=\log(x-3)+2$

I am so confused. I think the domain is $x>3$ but is the range ARN or is it $y>0$ . . .
10
votes
2answers
244 views

$\lfloor n^{1/2}\rfloor+\cdots+\lfloor n^{1/n}\rfloor=\lfloor \log_2n\rfloor +\cdots+\lfloor \log_nn \rfloor$

Prove that: $\lfloor n^{1/2}\rfloor+\cdots+\lfloor n^{1/n}\rfloor=\lfloor \log_2n\rfloor +\cdots+\lfloor \log_nn \rfloor$, for $n > 1,\, n\in \mathbb{N}$ For example. For $n=2$, we have $\lfloor ...
2
votes
1answer
20 views

What is the number of real roots of $(\log x)^2- \lfloor\log x\rfloor-2=0$ $\lfloor\,\cdot\,\rfloor$ represents the greatest integer

Question : What is the number of real roots of $(\log x)^2- \lfloor\log x\rfloor-2=0$. $\lfloor\,\cdot\,\rfloor$ represents the greatest integer function less than or equal to $x$. I know how to ...
1
vote
2answers
41 views

Need help with a proof concerning zero-free holomorphic functions.

Suppose $f(z)$ is holomorphic and zero-free in a simply connected domain, and that $\exists g(z)$ for which $f(z) =$ exp$(g(z))$. The question I am answering is the following: Let $t\neq 0$ be a ...
0
votes
0answers
48 views

Creating a function with logarithmic growth

I have some knobs with an internal value of $0$ to $1$. These represent a value in a range, like $1$ to $1000$. Case in point, I would like to be able to change the scale/growth of the display value. ...
0
votes
0answers
41 views

Comparing growth rates of functions using logs?

Suppose we have two functions $f(n) = n^{\log \log n}$ and $g(n)=\log n^{\log n}$ and we want to compare their growth rates. I'm using the flowing approach. Please tell me is it right or wrong? ...
2
votes
4answers
86 views

graphing $f(x)=x \ln \left(1+\frac{1}{x}\right)$

I was assigned to draw the graph of this function $f(x)$=$x\ln(1+{1\over x})$. And when I calculate $\lim_{x\to \infty} f(x)$ I get $1$ but the teacher it's not correct even though its graph on the ...
0
votes
1answer
68 views

For $0<a<b$, show $1-\dfrac{a}{b} < \log\left( \dfrac{b}{a} \right) < \dfrac{b}{a}-1$

Prove that if, $0 < a < b$ Then $1-\dfrac{a}{b} < \log\left( \dfrac{b}{a} \right) < \dfrac{b}{a}-1$
2
votes
1answer
50 views

Show that $\operatorname{ln}(n!)=\Theta(n\operatorname{ln}(n))$

Another question about asymptotic approximations. We are asked to show that $\operatorname{ln}(n!)=\Theta(n\operatorname{ln}(n))$ I'm stuck tho and can use help. What I did is: ...
0
votes
0answers
32 views

check my short simple proof - Functions are of same magnitude. Asymptotic notation.

A simple question with a short solution I thought of, but I would like verification. $f(n)$ is a function that approaches infinity as $n$ approaches infinity. We are asked to show that ...
0
votes
1answer
30 views

Allowed values for $x$ in $\log_2(x)$

$$y=\log_2x$$ What are the allowed values for $x$ in this function? How do I calculate it? (I know how it works for normal functions with fractions and other stuff, but this one I'm stuck)
0
votes
2answers
825 views

Writing an equation for a log function given the graph

I have the following graph for a logarithmic function $f$: I don't know any thing about writing an equation for a logarithmic function by knowing it's graph. All what I know is how to draw a graph ...
0
votes
1answer
40 views

Minimum value of $ f(x) = x\log_2x +(1-x)\log_2(1-x) $ [closed]

What is the minimum value of the following function for $ 0<x<1 $ ? Here the base of logarithm is 2 . $ f(x) = x\log_2x +(1-x)\log_2(1-x) $
2
votes
1answer
84 views

Why isn't $\log(-1)$ defined?

Why isn't $\log(-1)$ defined. It can be defined as being equal to $i\pi$. Why don't we define the $log$ function over Complex Numbers as well.
0
votes
1answer
42 views

function symmetric around a point

I need some quick help solving this: What is y(ln(2))if the function y satisfies $$\frac{dy}{dx}=1-y^2$$ and is symmetric about the point (ln(4),0)? I know that a function is symmetric about the ...
0
votes
2answers
46 views

Use a graph to estimate the time at which the number was increasing most rapidly

For the period from 2000 to 2008, the percentage of households in a certain country with at least one DVD player has been modeled by the function $f(t) = \frac{87.5}{1 + 17.1e^{−0.91t}}$ where the ...
1
vote
1answer
45 views

At which parameter value $c>0$ do the number of solutions of $\log(1+x^2)=x^c$ change?

I'm looking at the functions $x\mapsto \log(1+x^2)$ and $x\mapsto x^c,\ c>0$ on the interval $\mathbb R^+_0$. I'm interested in the properties of $$\log(1+x^2)=x^c.$$ Graphically, for small $c$, ...
0
votes
1answer
86 views

Expressing logarithms as ratios of natural logarithms

$$\frac{\log_2 x}{\log_3 x}=\frac{\ln x}{\ln 2} \div \frac{\ln x}{\ln3}$$ Why can logarithms be written as ratios of natural logarithms? Can you explain it abstractly, please? Example of an ...
1
vote
1answer
47 views

Understanding a question on iterated logarithms

I have in front of me a math problem that I do not understand. That's to say, I don't understand what is being asked of me. Problem: We can define $\log_2**(x) = log_2*(log_2*(x))$ and the function ...
2
votes
1answer
39 views

Making logarithmic function go higher

I am looking at logarithmic functions, and, lets say, log2 (x+3) is having a bit of a growth rate between 0-10 values of ...
2
votes
1answer
69 views

Online logarithm drawing

I am looking for a site that will give me the output of my logarithms. What I want to do, is I want to input, in example log(2), and I want it to draw an output ...
1
vote
1answer
48 views

domain of function with logarithmic terms.

what will be the domain of function given below? $$y=1+3(\log(\sin(x))+\log(\csc(x)))$$ in book it is given this is valid for the values of angles of 1st and 2nd quadrant only. why this function is ...
1
vote
2answers
54 views

Find the inverse function…

So, I have the function $$f(x)=\frac{2^x-2^{-x}}{2}.$$ I tried finding the inverse function the usual way I do, but I guess I'm stuck with these degrees. So far, I've come to this form ...
1
vote
2answers
89 views

Filling in 'x' in a log function

if $3^5=x$ (exponential equation) converts to log form gives $log_3x=5$ that makes sense. $$ 3^5 = 243 \Rightarrow x=243 $$ So if I take the log form again: $log_3x=5$ and replace $x$ with $243$. I ...
4
votes
5answers
167 views

How do I solve such logarithm

I understand that $\log_b n = x \iff b^x = n$ But all examples I see is with values that I naturally know how to calculate (like $2^x = 8, x=3$) What if I don't? For example, how do I solve for $x$ ...
2
votes
1answer
42 views

determining sign of function containing logarithm.

I would like to know the sign of the following term in general. I tried approximately and it was negative. Is there any $m_0$ such that for all $n>m>m_0$, the following function is positive or ...
1
vote
0answers
36 views

What's the most straight forward way to show that a function is increasing?

I am trying to show that: $$\frac{2}{n}\log\Gamma\left(\frac{x}{2}\right) - \log\Gamma\left(\frac{x+n-1}{n}\right)$$ is an increasing function for $x \ge 5$ and $n > 2$ One way to do this would ...
1
vote
1answer
224 views

Comparing rates of change: which function increases faster?

I am comparing two functions for $x \ge 1$: $$f(x) = \ln(\lfloor\frac{x}{9}\rfloor!) - \ln(\lfloor\frac{x}{10}\rfloor!) - \ln(\lfloor\frac{x}{90}\rfloor!)$$ $$g(x) = (2.07766)\sqrt{\frac{x}{9}} + ...
1
vote
2answers
62 views

Logarithm calculation result

I am carrying out a review of a network protocol, and the author has provided a function to calculate the average steps a message needs to take to traverse a network. It is written as ...
0
votes
1answer
250 views

Function design: a logarithm asymptotic to one?

I want to design an increasing monotonic function asymptotic to $1$ when $x\to +\infty $ that uses a logarithm. Also, the function should have "similar properties" to $\dfrac{x}{1+x}$, i.e.: ...
1
vote
1answer
95 views

Expansion of Lambert $W$ for negative values [duplicate]

What is a good approximation for the Lambert $W(x)$ function for values between $\frac{-1}{e}$ and $0$? Is it simply $x-x^2$? If so, what bounds are there on the error?
2
votes
0answers
459 views

Log-concave functions whose sums are still log-concave: possible to find a subset?

Rationale: I am puzzled by a problem of log-concavity, which arises in population dynamics where the curvature of the logarithm of sums is a quantity of interest. It is well-known that sums of ...
0
votes
2answers
54 views

For what $f(n)$ does $O(f(n) \log n)=O(\log\log n)$?

$k=f(n)$. Given $O(k \log_2 n)$, what function $f$ of $n$ would be needed for it to equal $O(\log_2 \log_2 n)$? (where $k \in n \in \mathbb{Z}^+$)
1
vote
2answers
81 views

Derivative for log

I have the following problem: $$ \log \bigg( \frac{x+3}{4-x} \bigg) $$ I need to graph the following function so I will need a starting point, roots, zeros, stationary points, inflection points ...
2
votes
1answer
20 views

Estimation for large $k$.

I have a function $f(k)$ defined on the set of natural numbers and I managed to show that $f(k)>n-\binom n k(1-n^{-2/3})^{k(k-1)/2}$ for all integers $n\ge k$. I am hoping to get a further ...
3
votes
3answers
5k views

The relation between an exponential function and a logarithmic function

I have been told multiple times that the logarithmic function is the inverse of the exponential function and vice versa. My question is; what are the implications of this? How can we see that they're ...
0
votes
2answers
94 views

How have they simplified this function?

I have been trying to figure out how the following has been simplified, but I am getting nowhere with it. Anyone have any ideas? $9(n/3)^{5/2}$ to $(1/3)^{1/2} f(n)$ It is given that $f(n) = ...
1
vote
1answer
146 views

Finding the Function to a log-log plot

My maths is not very good, so please bare with me if the answer is obvious. I have a log-log plot below, which I have generated in R. I now need to find what i believe to be called the inverse to ...
0
votes
1answer
73 views

Could you describe this function as “logarithmic”?

Consider the following function: $$f(x) = \frac{1}{\sqrt{x}}$$ As $x$ increases, the value of $f(x)$ decreases, but the decrease tapers off quickly as $x$ gets larger, and if you plot the graph of ...