Log Definition and 618 Threads

I haven't used a log table in a long time and the one I used in High School went from 10 to 99 with four significant figures for the logarithms. I wondered how did Briggs create a log table 400 years ago? How did he find the logarithm of 7(base 10)? I looked around the internet and You Tube and...

I started off by using law of logs to divide the logb (6x/18) but i dont know what to do after, please help.

In another thread the concept of how many seconds in a year came up and it made me think of putting milestones of a human lifetime on a log scale. Units are seconds. Please feel free to amend or change or just make it better. Maybe an actual plot? What strikes me is most of life is in the last...

Let ##A, B\in M_n(\mathbb{R})## be positive definite matrices. Prove that for ##0\le t\le 1##, $$\det(tA + (1 - t)B) \ge \det(A)^t\det(B)^{1-t}$$

Hi, I tutor maths to High School students. I had a question today that I was unsure of. Can the natural log be to the base 2? The student brought the question to me from their maths exam where the question was: Differentiate ln(base2) x^2 If the natural log is the inverse of e then how does...

Hi, This is a pretty simple question, but I am new to Mathematica so I am not sure if I am missing something obvious. Question: How do I make the expression ## e^{log(z)} ## return z? Attempt: I have used all of the following combinations and all of them return ## e^{log(z)}##. Are there any...

My log burner is just too powerful for everyday use. It is spec'd at 5kW and has an area of about 200X400mm. It's a single fuel design with no bottom vent. The air control is quite clever. It has an 'air curtain' supply which comes down from the top and two adjustable slots in the doors to get...

solve $e^x-\ln{x}=4\quad x\approx1.48 \quad x\approx 005$ ok I could only do this with a calculator but need steps

This was the question, The above solution is the one that I got originally by the question setters, Below are my attempts (I don't know why is the size of image automatically reduced but hope that its clear enough to understand), As you can see that both these methods give different answers...

My wife cannot log onto Wells Fargo account. She talked to the WF assistants, they directed her to delete cookies and history. Still doesn't work. She tried on my computer, it works. So problem is on her computer. She uses FireFox, I went in, deleted ALL history( thousands of them), I deleted...

I'm not sure how to get this first derivative (mainly where does the 4 come from?) I know x̄ is the sample mean (which I think is 1/2?) Can someone suggest where to start with finding the log-likelihood? I know the mass function of a binomial distribution is: Thanks!

I found vlog=1.9/t and vb-v=1.15/t and vb+v=d+1.15/60.8 don't know what to do now

Hello, I'm trying to follow Wolfram to do a least square fitting. There are multiple summations in the two equations to find the coefficients. Are the i's the same in this case? Thanks!

I got stuck when i eliminated the parameter.

I was watching this video about how they invented log tables and some things I do not understand. At 5:12 he changes the scaling from 1's to 10's I don't understand how this is allowed. The number represents the number of times the base was multiplied by itself. In the seconds before this...

I have never used induction to justify the derivative to a function, so I don't know where to start. Does anyone have some tips?

Hi, I am trying to solve the following equation: ##\mathbf (t_s + t_wm)log(p)+ 2t_h (\sqrt{p} - 1) ## ##\mathbf (10+0.01 * 1000) log(36) + 2 * 2(5) ## I think log(36) would be 18. Note log is ##\mathbf log_2 ## Somebody please guide me. Zulfi.

Given ln(ab) = b⋅ln(a) Then ln(1x) = x⋅ln(1) Also ln(2x) = x⋅ln(2) Say ln(2x) = ln(1x) Then Also x⋅ln(2) = x⋅ln(1) But, dividing both sides by x ln(2) ≠ ln(1) Similarly, x⋅ln(2) = x⋅ln(1) Dividing both sides by x and ln(2) 1 ≠ 0 But we know x = 0 as per the original statement...

Homework Statement Determine function $$f(x) = \log(\sqrt{x^2+1}+x)$$ Is odd or even. Homework Equations ##\log(a+b) = \log(a) + \log(1+b/a)## The Attempt at a Solution First I thought it is a even function without considering the x at the end, which of course isn't the actual case. Then I...

Hi, in this link https://math.stackexchange.com/questions/2605752/proof-log-convex-implies-convexity , there is a theorem that labelled with yellow. I do not know the name of theorem and would like to know it's derivation. Could you please help me?

Homework Statement "Find ##\int_0^x \frac{6\ dt}{2t+1}##." Homework Equations ##\int \frac{\ dx}{x} = \ ln(x)## for ##x>0## The Attempt at a Solution Method 1: Let ##u=2t+1##, ##\frac{1}{2} du=\ dt##. ##\int_0^x \frac{6\ dt}{2t+1}=3\int_1^{2t+1} \frac{du}{u}=3\ ln(u)|_1^{2t+1}=3\ ln(2t+1)##...

Recently I saw this clip on YouTube which has a revolutionary idea of mathematical notations,What do you think about it?

Homework Statement Using log taylor expansion to express cumulants in terms of moments I have worked through the expansion- ##log(1+\epsilon)= ...## see thumbnail- and that's ok; my question is why does the expansion hold, i.e. all i can see is it must be that ##k## is small- how is this...

Homework Statement Show that ##\sum_{n=1}^{\infty}\frac{\log (1+1/n)}{n}## converges. Homework EquationsThe Attempt at a Solution If I take for granted the inequality ##\log (1+1/n) < 1/n##, I can easily show that this converges. My problem is is that I am not seeing how to prove convergence...

I'm learning complex analysis right now, and I'm reading from Joseph Taylor's Complex Variables. On Theorem 1.4.8, it says "If a log is the branch of the log function determined by an interval I, then log agrees with the ordinary natural log function on the positive real numbers if and only if...

I just asked a similar question, but I got help for that one, and now I am stumped again. I need to find the domain for $$f(x) = ln(x^2-5x)$$ What's confusing me is how to deal with the exponent. I can't think of a way to get around it.

Hi, My Android ZTE phone is not loading the OS, not completing POST andgiving me an Android Recovery error message . How can I read/use log files to recover phone? Here is the error message, and the files listed in it, which I can access using on/volume keys (On key selects, Volume allows me...

Dear Everybody, I am having troubles figuring out why the plus or minus sign in this problem. The question is: Solve the equation $\sin\left({z}\right)=2$ for $z$ by using $\arcsin\left({z}\right)$ The work for this problem is the following: $\sin\left({z}\right)=2$...

What is the difference between log and ln?? [Thread moved to General Math forum by moderator]

here is a link with the formula: https://portal.uea.ac.uk/documents/6207125/8199714/steps+into+calculus+integration+and+natural+logarithms.pdf i'm talking about the formula that says the integral of f'(x)/f(x)dx = ln(f(x))+C it's kind of hard to put this into Google. where does this formula...

Homework Statement Homework Equations Pitagora's: ##~a^2+b^2=c^2## Maxima/minima are where the first derivative is 0 The Attempt at a Solution $$\left( \frac{a}{2} \right)^2+\left( \frac{b}{2} \right)^2=r^2~\rightarrow~b^2=\frac{16r^2}{a^2}$$ The strength S has the proportion coefficient k...

Homework Statement Homework EquationsThe Attempt at a Solution C is the point of contact and G is the CM of the plank . x be the distance between G and C .Since plank always remain in contact , x=aθ When the line joining the point of contact C with the center makes an angle θ with the...

In simple words, what is the difference between log and ln?

Good afternoon guys, I want to discuss with you guys a few things... So i already design a log cutting mechanism as you can see in the picture below. But there is so much defect on my mechanism.. The biggest thing that stressed me out, its still uneasy to use because after cut the log, the user...

Good morning guys, So i want to make mechanism to cut log with diameter 5 cm and 120 cm length. So how i can calculate the force to cut this log perpendicular and paralel. What is tbe formula i can use? And how i can determine the saw thickness and rpm needed to cut this log? Thanks guys for...

I just wanted to double check that I was doing this right ( if the math in my process makes sense). Question: Solve for x given the following equation. eex= 2 I found the ln of both sides, so : ex= ln2 and then found ln again x= ln(ln(2)) Was this the correct way of doing this? I...

Hi I have the following equation: Log(x/y)=A*(e^z(-1)) I know values of y, A, z. I need to calculate x from this equation. I need to ‘extract’ x first therefore Log(x)-Log(y)= A*(e^z(-1)) Log(x) = A*(e^z(-1)) +Log(y) x=10^[ A*(e^z(-1)) +Log(y)] I am not sure whether my formula modification...

Homework Statement I'm having a hard time differentiating when to use log instead of ln, vice versa. Are there any general rules to follow? For example I have to evaluate 4u^-3 + u^-1. Homework Equations f'(1/u) = log u f'(1/u) = ln u The Attempt at a Solution I put -2u^-2 + log(u) but the...

Homework Statement Homework Equations log_2 x = y 2^y = x 3^2^y The Attempt at a Solution log_2 x = y 2^y = x log_2 {log _3 {log _2 { log_3 {2^y} } } } what am I suppose to do?

Hi, I'm looking for a visual proof log(ab) = log a + log b I've seen diagrams where the values are measured out, but it's not immediately obvious why this holds. Is there an intuitive way to illustrate this? Also, are there other functions with this property.

Solve the log equation log_16 (3x-1)=log_4 (3x) + log_4 (0.5) Can someone get me started? The left side has base 16 and the right side base 4. How is this done when two different bases are involved?

I have this integral that when solved, involves squares and natural logs, where ##A\,##,##\,b\,##, and ##\,x_e\,## are constants while ##x## is a variable. ##A = \int_{x_e}^{x} \frac{x^2 - b^2}{x} dx = \int_{x_e}^{x} x \, dx -b^2 \int_{x_e}^{x} \frac{dx}{x} = \frac{x^2}{2} - \frac{x_e^2}{2} -...

If y=sin5 + log base 10 x + 2 sec x find dy/dx Please solve the problem

Hi, see attached PdF file for my question concerning serie expansion of log(z) at infinity. Thank you Belgium 12

Homework Statement $$ln(x^2)=4$$ Homework Equations ##a^{log_a(x)}=x## ##log_a(a^x)=x## The Attempt at a Solutionln(x^2)=4 <=> ##2ln(x)=ln(4)## <=> ##ln(x)= [ln(4)]/2## <=> ##log_e(x)= [ln(4)]/2## <=> ##e^{ln(4)/2}=x## <=> ##[e^{ln(4)}]^{1/2}## <=> ##sqrt(e^{ln(4)})##...

Trying to complete some homework help I got a bit stuck on an elementary or common problem that was always a bit difficult. I have a function f(x) and just want to plot log f(x) against log x. This is common in chemistry and biochemistry. It should have been easy. :redface: I have picked up...

Could someone please explain to me why this equation holds: alog x = blog x / blog a For all the all other rules concerning logarithms I could derive them from the rules for exponentiation, except for this rule. Could someone please explain to me how this derivation works? And how the value of...

Homework Statement Hello! I am trying to compute the bi-geometrical mean on data that contains negatives. But before that I wanted the test the formula that accounts only for positive values using the sum of their logarithms. By doing so I don't get the result I compute by using the "usual" geo...

If we have log 3 (x+9) + 2 = y. It states that we have a HT 9 units left and 2 units up. But if we manipulate that too log 3 (x+9) = y - 2 And convert to Exp form. This gives me 3^(y-2) = x + 9 or 3^(y-2) - 9 = x This looks to me more like a HT 2 units right and a vt 9 units down. I don't...

½Logb(x2-1)≈logb(x) This is an easy and useful way to calculate the log of any natural number, including primes, it won't ever give a precise result, obviously (because of the -1), but as "x2-1" will always have divisors smaller than "x", you can easily calculate the approximation by using the...