All Questions
Tagged with logarithms graphing-functions
157
questions
0
votes
2
answers
35
views
Logarithm approximation loses solution
I was doing an exercise in which I had to plot by hand a function.
The function was $$f(x)=\ln\left(\frac{\sqrt[3]{x}}{3x - 1}\right)$$
which I rewrote into $$f(x)=\frac{\ln\left(x\right)}{3} - \ln\...
- 135
0
votes
2
answers
39
views
How do I move the origin of a logarithmic spiral?
Context: I'm a high school junior (in pre-calculus) and I'm trying to teach myself how to graph a logarithmic spiral for a math/art project.
Basically, I need to move the center of a spiral from the ...
1
vote
2
answers
71
views
Is $y = (\log x)^u$ faster than $y = x$ for any $u$?
If $(\log x)^u\over x$ converges to a constant as $x \rightarrow \infty$, then the set $S$ of possible values of $u$ is
(A)$[-1,1]$
(B)$(-\infty,1]$
(C)$(-\infty,\infty)$
(D)None of the above
Here's ...
1
vote
0
answers
24
views
Why is it more common to draw in arithmetic subdivisions in logarithmic plots?
I can understand that you'd sometimes want to see where the linear subdivisions are on a logarithmic plot, and track e.g. where one y-value is ~3 times as large as another y-value (e.g. 2x10^5 ...
- 135
0
votes
2
answers
59
views
$g(n)$ upperbounds $f(n)$ but graph shows otherwise
Given we have the following functions:
$$f(n)=\log_{2}^{4}n$$
$$g(n)=2^{\sqrt{\log_{2}n}}$$
I've done the limit of f(n) over g(n), and found that g(n) is an upperbound of f(n) given the zero result:
$$...
0
votes
0
answers
165
views
how to draw graph of X / ln(x)
My question is to draw the graph of x/ln(x) ;where ln represents natural log.
I know that the graph will decline from x= 0 to 1 and at 1 there will be an asymptote but I don't know what will the ...
- 11
0
votes
2
answers
92
views
Understanding how a log-log plot models an electronic component
In a research paper (available here) that I'm reading, there is a description of the behavior of a photo resistor used in the construction of a more complex sensor, that goes like this :
Its ...
1
vote
1
answer
142
views
What does graphical solution really mean?
Given question is "Sketch the graph of $y=ln(2x-1)$. Determine the equation of the straight line which would need to be drawn on the same axes as graph of $y=ln(2x-1)$ in order to obtain a ...
0
votes
2
answers
42
views
Find the intersection of the graphs $y=2^{x-a}-1$ and $y=a\log_2(x-a+1)$
With $a$ being a real number, the graphs of the two functions $y=2^{x-a}-1$ and $y=a\log_2(x-a+1)$ intersect in $A\in Ox$ and $B$. When the area of $OAB$ is $\dfrac{7a}{2}$, find the coordinates of ...
- 311
2
votes
1
answer
48
views
Why does the graph of $-\left(x\right)\log_{2}\left(x\right)-\left(1-x\right)\log_{2}\left(1-x\right)$ look like: $\cap$?
I can understand it algebraically, but I wanted some geometric-esq intuition for why the graph is this way. Like some intuition that I could've used to derive it.
This is the plot:
I eked out some ...
1
vote
2
answers
74
views
How to find inverse function for following logarithm function?
I am kind stuck with finding the inverse function of following function.
$$f:x\mapsto\log_2(x^2-3x-4)$$
Let $y =f(x)=\log_2 (x^2 - 3x-4)$. After I simplify the function, I end up with:
$2^x = y^2 - 3y ...
- 111
2
votes
1
answer
224
views
How to linearize a base-10 exponential function
I have a base-10 exponential function with the equation:
$$y = 0.000346 \cdot 10^{0.00676x} + 0.148$$
I am trying to linearize this equation but unable to do so. I tried taking $\log(y)$ in the $y$-...
0
votes
1
answer
990
views
Finding the Equation of a Straight Line on a Semi-Log Plot Given Two Points
I want to learn how to create a straight line on an Excel semi-log graph of my data. An internet search pointed me to a similar answer on math.stackexchange.com: Finding the Equation of a Straight ...
- 11
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
2
answers
31k
views
How to type logarithmic functions into Desmos graphing calculator?
Does anyone know how to type logarithmic functions into Desmos graphing calculator (https://www.desmos.com/calculator) ?
I need to type a function, in which y equals to logorithm of 10 with the base ...
- 828