Questions tagged [logarithms]
Questions related to real and complex logarithms.
10,258
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Find the point of intersection of an annuity and an investment
We were completing some classwork for Annuities and finding the Sum of a G.P for simple situations as well as finding the time take for an annuity to reach a given value.
Given the context we wanted ...
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How to solve for a value in a log
I have a formula:
Weight=onerepmax*(0.488 + 0.538 * ln(-0.075*reps))
And I need to solve for reps given a onerepmax and a weight.
I got as far as:
...
- 113
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Determining the witnesses (constants $C_0$ and $k_0$) when showing $(log_b n)^c$ is $O(n^d)$ (b > 1 and c,d are positive)
I'm having a hard time finding the constants/witnesses $C_0$ and $k_0$ that show $(\log_b n)^c$ is $O(n^d)$. That is $|(\log_b n)^c| \leq C_0|n^d|$ for $n > k_0$ (b > 1, and c,d are positive).
I ...
- 883
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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
votes
3
answers
87
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Is there any other function than $log$ for which $f(ab) = f(a)+f(b)$ and $f$ is monotonic? [closed]
Is there any other function than $log_{x}$ for which $f(ab) = f(a)+f(b)$ and $f$ is monotonic?
If the answer to this question is yes, how can I find such functions?
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How would you prove $\log_{2}x < \sqrt x$ for $x > 16$? [closed]
I'm not really showing how to prove this, since I tried finding the $x$-intercepts/zeros of $f(x) = \sqrt x - \log_{2} x$ , and see that $x = 4, 16$ work but inspection, but I'm not sure how to ensure ...
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How do you solve this equation $ \log_{2}(x) = \sqrt x$? [closed]
Disclaimer: Guys before voting to get the question closed I strongly feel we should instead have a feature on MSE that can merge such similar/duplicate questions since we got some really cool/through ...
- 883
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Solving $\frac{\ln(y/x)}{y-x} = t$ for $x$ [duplicate]
I am having trouble solving an algebra formula which is for a project of mine.
I must solve for $x$ ($y$ is a known value).
$$\frac{\ln\left(\dfrac{y}{x}\right)}{y-x} = t$$
As I try to solve the ...
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Find $\arcsin c$, $\, c\in\Bbb C$ [duplicate]
A math fan sent me a solution of the weird equation $\sin z=2$ posted in Quora. It is Weird because in real calculus, we experienced that $-1\leq \sin x\leq 1$. I saw this question in so many places ...
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Why is logarithm with base 10 having number greater than 1 always positive? [closed]
Consider logarithm with base 10 and number k
Why will it always be positive if k>1 and negative if k<1?
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2
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How to calculate the limit $\lim_{x \to 0}\frac{\ln(1 + \sin(12x))}{\ln(1+\sin(6x))}$ without L'Hôpital's rule?
$$
\lim_{x \to 0}\frac{\ln(1+\sin12x)}{\ln(1+\sin6x)}
$$
I know it's possible to calculate this limit just by transforming it; I think you need to use the knowledge that
$$
\lim_{x \to 0}\frac{\ln(1+x)...
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2
answers
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Why the property of exponents holds true even for fractional powers
How can we prove that the property of exponents a^m × a^n =a^(m+n) (where "^" this sign denotes the power a is raised to)holds true even if m, n and a are fractions? Like I can clearly see ...
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Unexpected asymptotic logarithm behavior
I have recently seen a rather confusing asymptotic property of logarithms:
$$
\log(n^4 + n^3 + n^2) \leq O(\log(n^3 + n^2 + n))
$$
I find this very unintuitive. Why would the log of a bigger ...
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Why the log function is so important on the plane?
I am studying right now some Complex Analysis and I have seen the importance of the (complex) logarithm function in almost every subject in it. Now I'm intrigued with that (possible) relation between $...
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When Does ((n^a)-1)/a)) Equal e; A Sophomore's plight
I am a high school student (sophomore) and have come across something I would like explained.
I was watching 3blue1brown for an explanation of calculus, when he used the formula: lim a->0 (d/dx(n^x)...
