All Questions
71
questions
-5
votes
2
answers
85
views
If the domain of $f(x)$ is $(-3, 1)$, then what is the domain of $f(\ln x)$? [closed]
I need a clear explanation for this question:
If the domain of $f(x)$ is $(-3, 1)$ then the domain of $f(\ln x)$ is ...
a) $\;(e^{-1}, e^3)$
b) $\;(0, \infty)$
c) $\;(1, \infty)$
d) $\;(e^{-3}, e^...
1
vote
2
answers
72
views
Log X to what base n yields a whole number [closed]
Does there always exist a real number 'n' such that $log_{n}x$ is a whole number for any real number x?
If yes what would the function to find this number look like?
- 11
1
vote
2
answers
30
views
Getting the domain of a real function with iterated logarithms [duplicate]
I would like to find the domain of the function
$$f(x)\:=\: \log_4\,\log_5\,\log_3\big(\,18x - x^2 - 77\,\big)$$
as a subset of $\mathbb R\,$.
I looked at the solution of the above problem, and it ...
- 356
0
votes
1
answer
67
views
Solutions to Some Logarithmic Inequalities
Suppose we have an inequation as shown below:$$I_0:\space \ln (x) > \frac{x-2}{x}$$ Now we would like to find the largest set $S$ of real numbers such that any element $p\in S$ will satisfy $I_0$ ...
3
votes
0
answers
78
views
What functions satisfy $f(ax) - f(a(x-1)) > f(b(x+1)) - f(bx)$ for all $a, b \in \mathbb{R}^+$ and $x \in \mathbb{Z}^+$.?
I am looking at a family of functions $f : [0, \infty) \rightarrow [-\infty, \infty)$ satisfying the following property:
$$f(bx) - f(b(x-1)) > f(a(x+1)) - f(ax) \quad \text{for all $a, b \in \...
- 31
1
vote
1
answer
111
views
How to prove $x^{\ln x} > \frac{x}{2} + \frac{1}{2x} $?
How to prove the following? $$x^{\ln x} > \dfrac{x}{2} + \dfrac{1}{2x} \tag{1} $$ for all $x \in \mathbb{R}^+\setminus \{1\}$?
I could prove $ x^{\ln x} > x $ and
$ x^{\ln x} > x/2 $ (in ...
- 3,227
0
votes
0
answers
50
views
Solution of Two Functions
Given $f(x) = -1 + 5(1.02)^x$ and $g(x) = \ln(3 - x)$, for what value of $x$ does $f(x) = g(x)$? I have been trying to solve this question for quite some time and I always seem to hit a dead end. What ...
- 11
0
votes
1
answer
83
views
Why is (log y) = m(log x) + c a straight line? (TMUA question)
In the TMUA (Test of Mathematics for University Admission) specimen paper 1 there is the following question:
The solution provided is as follows:
I am having trouble understanding the opening ...
- 29
1
vote
2
answers
103
views
Why is Desmos not showing $\ln(y)-\ln(y-1)$ as the same as $\ln(y/(y-1))$?
Desmos link.
The first two equations are equivalent and I can see this since both lines perfectly overlap:
According to my understanding and spreadsheet, the left side of the second equation, $\ln(y)-...
- 2,266
1
vote
5
answers
261
views
Is it possible to solve the equation $x - 1 = x^{-y}$ explicitly?
I'm trying to solve the equation
$$
x - 1 = x^{-y}
$$
or to find the inverse of the function that is represented by this equation - both explicitly (symbolically).
However, I cannot find a way to do ...
- 31
2
votes
1
answer
92
views
Challenge: Solve $x^x = \frac{1}{256}$ without the use of the Lambert W function
As stated above: $x^x = \frac{1}{256}$, solve for $x$.
Since $256$ is power of $2$, I let $x = 2^n$, where $n \in R$.
So:
$2^{n^{(2^n)}} = 2^{-8}$
$n*2^n = -8$
$-n = 2^{3-n}$
$\log_2$$(-n) = 3-n$
$\...
- 1,190
1
vote
2
answers
105
views
In the function $f(x)=k\ln(ax+b)$ what does the $k$ value represent?
Basically what the title of the question is, in the function $f(x)=k\ln(ax+b)$ I presume that $a$ is the slope, $k\ln(b)$ is the y intercept but what is $k$?
user1030904
0
votes
0
answers
30
views
What if a point in $[a,b]$ does not lie in the domain of $f(x)$ while applying IVT
I came across the function $f(x)=x^3\ln(\sin x)$. I tried applying IVT in the interval $\left[-\frac{5 \pi}{4},-\pi\right) \cup\left(0, \frac{3 \pi}{4}\right]$.
Now we see that
$$\begin{aligned}
f\...
- 10.2k
-1
votes
1
answer
85
views
A difficult problem concerning functional equations: $ f ( x ) f ( y ) = x ^ a f \left( \frac y 2 \right) + y ^ b f \left( \frac x 2 \right) $
While studying functional equation, I came across the following problem.
Problem. find all functions $ f : \mathbb R \to \mathbb R $ such that for some $ a , b \in \mathbb R $,
$$ f ( x ) f ( y ) = ...
- 123
2
votes
2
answers
160
views
Given $T = 75e^{-2t} $ then find $t$ as a function of $f(T)$
First off, I'm sorry if some terms are wrong because I speak Spanish and I don't know how to translate them to English properly.
I'm studying computation, and I have this problem from an integral ...
user835162