So, you'd have f(x)*f^-1(x)=1
You need to find f^-1(x). You can just plug in f(x) as given and then solve
Lol I'm dumb. This is probably looking for the function inverse. I have no clue how to explain that one, tbh
didnt u just explain function inverse
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No, I explained multiplicative inverse
Someone explain to me why we need logs to find how loud something is
Because logarithmic scales are really useful for measurements that are most often used in ratios. Decibels are a logarithmic unit, though we could define a non-logarithmic unit for volume. It just wouldn't be as easy to use in terms of the computations you want to do
This and because of the way the ear works. The ear doesn't "hear linearly." The range of human hearing is better represented by a logarithmic scale.
Think about it this way: if you take 100 steps back from a very loud source, it's not noticeably quieter, right? A logarithmic scale doesn't show a substantial difference between the volume initially and 100 feet away for the loud source. A linear scale would.
Similarly, a very quiet source 100 feet away should have a huge difference in the measured volume, much more than the very loud one. A logarithmic scale reflects this
Because omnidirectional emitters (of light and sound) act like spheres and without acoustic boundaries the number of "rays" from the origin of the sphere that hit you in relation to distance follows the inverse square law.
Surface area of sphere grows by factor of R^2. (If you want to prove it or something)
Yeah, but you can still use a linear unit for this. We use logarithmic here to match the range of the ear
I'd say that makes you more right, but the eye also detects light intensity logarithmically and probably evolved that way because of how light and sound tend to behave.
Your answer more directly addresses the original question.
Maybe. There are plenty of evolutionary examples of things with much higher and much lower dynamic ranges. And the difference between our dynamic range for hearing vs sight is huge: ~140 dB v. ~90 dB, respectively.
Eh, yours answers the same question, just from a different perspective. I just figured he might want an explanation related to the intuition of why logarithmic units were chosen based on physical experiences, rather than the technical math
The same thing is true for sight.
The dimmest to the brightest things we can see have been a problem for the movies forever.
What do you plan on doing with this tremendous power you wield?
That was a level 14 geometry problem. I am more than a man
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I will obtain level 25 in pre algebra soon