All Questions
19
questions
1
vote
2
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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
0
votes
0
answers
114
views
How to graph logarithm
I have the following question: Sketch the image under the map $w = \log z$ of $|z| = 1$.
I know that its a unit circle and by the definition $\log z=\log |z|+i \operatorname{Arg} z, \quad z \neq 0$ . ...
- 177
-1
votes
1
answer
563
views
Why is $\frac{1}{\ln(0)} = 0$?
Why is $\frac{1}{\ln(0)} = 0$?
I thought $ln(0)$ is undefined.
The context is, I am looking for discontinuities in a function, and I expected $x=0$ to be a discontinuity since $ln(0)$ is undefined. ...
- 29
0
votes
2
answers
116
views
Why are $e^{-4\ln(-x)+4}$ and $e^{-4\ln(-x)}$ positive?
Algebraically, why is $e^{-4\ln(-x)+4}$ a positive result but $e^{-4\ln(-x)}$ a positive result?
It seems like with logarithmic properties, they should both be negative, but Wolfram Alpha shows the ...
- 67
2
votes
3
answers
2k
views
How to find the Graph of a Logarithm from two Points
I have a graph of a logarithm function with only two points marked. I need to find the equation for the function from these two points. The two points are $(8,3)$ and $(1,0)$. I already know the ...
- 1,661
1
vote
2
answers
96
views
How to plot implicit function $\log_{10}{(xy-1)} = \log_{10}{((1-x)(1-y))}$
I'm inspecting various function and try to plot their graph based on my observations and compare with graphing tools afterwards.
Given an implicit function $\log_{10}{(xy-1)} = \log_{10}{((1-x)(1-y)...
- 5,411
2
votes
5
answers
297
views
Why is wolfram plotting a wrong graph for $f(x) =8^{\log_{8}({x-3})}$?
I'm manually plotting various functions' graphs and use desmos and wolfram to validate whether I've analyzed the function in a correct way. But then I came to the following function and it seems that ...
- 5,411
0
votes
1
answer
54
views
How is a function defined that contains a log of a number that can get negative?
I came across a problem on Khan Academy that was about finding the graph of a transformed function. The (transformed) function is given by:
$$y = 3 \log_2(2 - x)$$
What I don't understand, how can ...
- 2,493
1
vote
2
answers
344
views
Trying to visualise the integral of $1/x$ given division by zero is undefined.
I know the integral of $1/x$ is $\ln(x)$. Now, I also know what these graphs look like visually.
I tried to "add power, divide by new power" and of course it's undefined.
My logic was to consider $x^...
- 187
0
votes
1
answer
144
views
Creating a logarithmic function with known $x-y$ axis intersections
I know that to plot a straight line that intersects the axis in point $(x_1,y_1)$,(x_2,y_2)$ one can use this equation.
$$(x_2-x_1)\cdot (y-y_1)=(y_2-y_1)·(x-x_1)$$
To be more specific if i want a ...
- 113
0
votes
1
answer
74
views
forming log equation from graph points
Okay so I need to form a logarithmic equation from the points (1960,4.7) (1964,5.1) (1968,5.4). I have 'guess and checked' to get the equation 2.7421 log(x-1950)+1.9579, and was wondering if there was ...
- 1
1
vote
1
answer
2k
views
Logarithmic Equation - Graph curved line
I'm recreating the graph picture below with equations. Using the online graphing tool "Desmos":
These are all the equations I have done so far, with there restrictions top stop at specific points.
...
- 149
1
vote
1
answer
2k
views
Graphing picture equations - Curve Lines
I'm basically trying to recreate the graph picture below. Using a online graphing tool "Desmos":
I managed to create the equations for the straight lines and circles for the sunset picture.
However, ...
- 149
2
votes
1
answer
64
views
Sketching Logs with Quadratic Terms
$\log(x^2+1) = y$
asymptote at $x^2+1 > 0$ and so there is no asymptote
$x$ and $y$ intercept at $(0,0)$
How do you know that the function goes both directions, and has a dip in the middle?
...
- 983
2
votes
0
answers
80
views
Is the following graph of the function $f(x) = \ln (2\sin \frac{x}{2})$ right?
In my text book about Fourier Analysis, $x$ ranges from $-\pi$ to $\pi$.I think when $x$ is from $-\pi$ to $0$, $\displaystyle \ln(2\sin\frac{x}{2})$ is meaningless. Why does the left part of the ...
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