Tagged Questions

Questions related to real and complex logarithms.

251 views

Interesting problem in logarithms

I know this place isn't for math problems/homework, and believe me I've been trying for a long time to solve this problem (45 mins to 1 hour) and besides I think many would find this useful or at ...
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I'm not great with logarithms so I'd appreciate some help with the following

How is it that $n^{\frac{1}{\log n}} = 10$. I understand that $10^{\log a} = a$ but I don't know how to make the correct algebraic manipulations. Note: Assume $log$ is base 10
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Forward Algorithm Hidden Markov Model matrix help [Discrete]!

So this may seem like a bioinformatics question but it is the math part that is giving me trouble. I'm using a Python package called YAHMM to model DNA sequences. I created a model with two states (...
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Is a dollar gain truly equal to a dollar lost?

Under the context of the asymmetrical nature of gain to a loss, as shown below, is 1 dollar gained truly equal to 1 dollar lost? If not how would you go about calculating the equalization ratio at ...
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Integral of $\frac{1}{2x}$

The integral of $\frac{1}{2x}$ is $\frac{\ln(x)}{2}$, but can't it also be $\frac{\ln(2x)}{2}$ or $\frac{\ln(3x)}{2}$? Is there a special reason for $\ln(Ax)$ to have identical derivatives?
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Why is $\ln(x^x)=x\ln(x)$ valid?

I know that $\ln(x^k)=k\ln(x)$ for any constant $k$, but why is $\ln(x^x)=x\ln(x)$. The exponent $x$ is not constant.
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How to solve $4x-\log(x) = 0$

I have a problem solving this equation: $4x-\log(x) = 0$. I can't seem to get this equation to a simpler form featuring $\log$s only or getting rid of the $\log$. Is there a way to solve it without ...
34 views

Best fit in logarithmic chart

I have several variances ($\sigma^2$) which value depends on the velocity ($v$). As you can see in the graph, if increase the velocity, the variance does the same. I am studying this dependency, but ...
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Evaluating Logarithmic Expressions

Evaluate: $$\log_4 \left(\dfrac{1}{256}\right)$$ I am not sure how to approach this since there is nothing set equal to it.
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Integration of (Tsiolkovsky) rocket equation

The (Tsiolkovsky) rocket equation states that the velocity of a rocket can be calculated as $$v(t) = v_0 \ln\frac{m_0}{m_0 - \dot m t}$$ where $m_0$ is the starting mass, $\dot m$ is the (constant) ...
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How to normalize data in another scale?

Let $A$ be a set of values $\{a_1,a_2,a_3,a_4,a_5\}$ where $a_1 = 2$, $a_2 = 1$, $a_3 = 4$, $a_4 = 1$ and $a_5 = 2$, so, the $avg(A) = 2$. I'm looking for a normalization where the values below the ...
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Finding how many solutions does $f(x)=\ln x-kx$ has for $k>\frac 1 e$ and logarithmic inequality question

Find how many solutions does $f(x)=\ln x-kx$ has for $k>\frac 1 e$. $f<0$ at $x\to \infty$ and $x\to 0$. The derivative has a solution only at $x=\frac 1 k$. So place that point in $f$ and we'...
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Simplifying Quadratic Equations In Logarithmic Form

$log_{10}(x^2-x-7)=0.1$ $log_{10}(x-8)=1-log_{10}(x+1)$ $log_{10}(x+9)=1+log_{10}(x+1)-log_{10}(x-2)$ Note: I solved them as follows: $x = 3, -2$ but the textbook i'm using said there was no ...
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Prove convergence of this generalized integral

Prove the convergence of $$\int_0^1 \left[\ln\left(1+\frac1x\right)\right]^a\mathrm dx$$ for $a>0$.
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Compute $\lim\limits_{n\to \infty} \ln(3n+7) - \ln(n)$

The reason why I'm having trouble with this problem is because it involves natural log (ln) and I need to find the limit. I need to find $\lim_{n\to\infty} \ln(3n+7)-\ln(n)$. I noticed that as $n$ ...
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Solve the logarithmic equation by $x$

Solve the eqation for all real $x$: $\log_2(x^2+7)+\log_3(x+6)=6$. What I tried: $\log_2(x^2+7)=a$ and $\log_3(x+6)=b$, then $a+b=6$ and $2^a=3^{2b}-4\cdot3^{b+1}+43$. But the problem is $a$ and $b$ ...
550 views

Solving for n, n is an exponent.

If you have a sequence of random numbers ranging between 1 and 64, what is the length of a sequence that will give a 98% chance of having at least one ( 1, 2, or 3) in the sequence? Here is the ...
Multi-variable calculus involving $\ln$
I am having difficulty with differentiating this equation with respect to $y$: $$W= x^{y \ln(z)}.$$ Differentiating calculators are giving me the answer $$\ln(x) \ln(z).x^{y \ln(z)}$$ But I can'...