# What is Logarithmic: Definition and 362 Discussions

A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale. Rather, the numbers 10 and 100, and 60 and 600 are equally spaced. Thus moving a unit of distance along the scale means the number has been multiplied by 10 (or some other fixed factor). Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph. Another way to think about it is that the number of digits of the data grows at a constant rate. For example, the numbers 10, 100, 1000, and 10000 are equally spaced on a log scale, because their numbers of digits is going up by 1 each time: 2, 3, 4, and 5 digits. In this way, adding two digits multiplies the quantity measured on the log scale by a factor of 100.

View More On Wikipedia.org
1. ### Solving a nested logarithmic equation

Problem statement : Let me copy and paste the problem on the right as it appears in the text. Solution : Using the Relevant Equations (2) and (3) above, we can claim that \begin{align*} &\log_{2x^2+3x+5}(x^2+3)=1\\ &\Rightarrow x^2+3 = 2x^2+3x+5\\ &\Rightarrow x^2+3x+2=0\\ &\Rightarrow...
2. ### Solve for ##x## in the given logarithmic equation

##\frac{1}{log_x 2}##+ ##\frac{1}{log_x 3}##+##\frac{1}{log_x 6}##=## 3.6## ##log_2x + log_3x+log_6x =3.6## ##log_2x ##+##\frac{log_2x}{log_2 3}##+##\frac{log_2x}{log_2 6}##=##3.6## ##log_2x ##[1+ ##\frac{1}{1.58496}##+##\frac{1}{2.58496}]##=##3.6## hmmmm it took me some time here to note that...
3. ### B Is Mean Temp in 2 phase Heat Exchangers Higher Than Logarithmic Mean?

Is Mean Temp in 2 phase Heat Exchangers Higher Than Logarithmic Mean? I am looking at this paper: https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1314&context=iracc Having a bit of trouble understanding all of it, but my basic question is just: If I have a heat pump where the hot...
4. ### I Logarithmic scale - interpolation

Hi, knowing the coordinates of two points: ##(x_1,y_1)## and ##(x_2,y_2)## on a linear scale plot, I can use linear interpolation to get ##y## for a point of known ##x## using the formula below: $$y=y_1+(x−x_1) \frac{(y_2−y_1)}{(x_2−x_1)}$$ But how does it look like in the case of logarithmic...
5. ### MHB (ask) Calculating Logarithmic Question

May I know how to calculate this question without a calculator? The final answer of this question is 3 but I really have no idea how to work on it to get the final answer.
6. ### B Logarithmic IV graphs of diodes

Hello there, I've been working through a task (that doesn't have an answer sheet or explanation) in which we plot I against V for three different diodes. Each has a different threshold voltage and displays the usual charcteristic curve. The final question is this: "It is suggested that the...
7. ### MHB [ASK] Logarithmic Equation

A friend asked me how to solve this question: log_2(x+2)+log_{(x-2)}4=3 I said I had no idea because one is x + 2 and the other one is x - 2. If both are x + 2 or x - 2, I can do it. He said that if that's the case, even at his level he could solve it. This is what I've done so far regarding the...
8. ### B Why is an inverse logarithmic scale chosen for the magnitudes of stars?

Star magnitudes of brightness seem to use inverse logarithmic scales, is there a benefit to this? Why was this chosen, i can understand logarithmic might make it easier to interpret data in same way we do similar for earthquakes etc. But why inverse ? When i look at a HR diagram for example (...
9. ### B Confusion about the domain of this logarithmic function

Should I just follow the original question? If given as ##f(x)=\ln x^4## then the domain is x ∈ ℝ , x ≠ 0 and if given as ##f(x) = 4 \ln x## the domain is x > 0? So for the determination of domain I can not change the original question from ##\ln x^4## to ##4 \ln x## or vice versa? Thanks
10. ### I Logarithmic terms in a system of equations

(I hope this is not a double posting) I want to solve this system of equations, containing logarithmic terms: ##7\ln(a/b)+A = 7\ln(d/e)+D = 7\ln(g/h)+G## ##7\ln(a/c)+B = 7\ln(d/f)+E = 7\ln(g/i)+H## ##7\ln(b/c)+C = 7\ln(e/f)+F = 7\ln(h/i)+I## ##a\phi_1+d\phi_2+g\phi_3=X##...
11. ### B Using a logarithmic scale to represent COVID-19 growth

The author, John Burn-Murdoch, shows here ( https://threadreaderapp.com/thread/1237748598051409921.html ) how the logarithmic scale can give a better "sense" of what is happening. In linear scales, some countries' data is squashed to almost nonexistent, while others explode out of control. I...

50. ### Oribit integrator for a logarithmic potential

Hello! Right know I'm trying to make an orbit integrator for solving a logarithmic potential with the form: $$\Phi= \frac{v_0^2}{2} ln(x^2+ \frac{y^2}{u^2} + r_0^2)$$ where v0, u, and r0 are constants My approach is to use, \ddot{q} =...