Questions related to real and complex logarithms.

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0
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1answer
18 views

Log power rule problem

According to many parts of the Internet, this log rule is used. log(a^b) = b*log(a) The proof is: Now let's say I want to use the rule in a Cartesian ...
0
votes
2answers
33 views

Linear equation from log equation

Further mathematics is driving crazy at the moment as I prepare for a PHD in chem eng. I've been working hard at the books but this one has caught me out. I basically need to derive a linear ...
0
votes
1answer
35 views

Finding x and y from two given logarithmic equations

I'm just studying some further mathematics units for my own benefit before I undertake a PHD in chemical engineering next year. I feel the learning of the mathematical concepts at this level will help ...
3
votes
5answers
158 views

Is the natural logarithm actually unique as a multiplier?

The Wikipedia page on the natural logarithm says: 'Logarithms can be defined to any positive base other than 1, not only e. However, logarithms in other bases differ only by a constant multiplier from ...
1
vote
1answer
14 views

$\lim_{x\to 0}x^a\log^k(x)$ where $a>0,k\in\mathbb N_0$

I'd know how to solve this for $k=0$ or $k=1$ for example, but I'm currently lost trying to prove the limit is zero for any non-negative integer $k$. I'd appreciate any hints!
2
votes
1answer
45 views

Why does $\ln x / \ln b = \log_b x$?

I'm doing some Java code. As far as I can tell, Java only has functions that do natural log and base $10$ log. I have a requirement to specify the base. I've seen that doing $\ln x/ \ln b$ is the ...
1
vote
1answer
36 views

Solving logarthmic equation [on hold]

I have been doing this problem for an hour now; however, I am not able to match my answer to the back of the book. I want to understand how to solve this problem. Someone pls help and explain how to ...
0
votes
1answer
9 views

Proving logarithmic maths graphically

I'm just going through some further maths units as I prepare for a PHD in chemical engineering. I'm finding the thought processes to be invaluable in my problem solving skills. However, I recently ...
5
votes
1answer
13k views

Why the number e(=2.71828) was chosen as the natural base for logarithm functions? [duplicate]

Possible Duplicate: What's so “natural” about the base of natural logarithms? Why the number e(=2.71828) was chosen as the natural base ...
61
votes
7answers
3k views

What's so “natural” about the base of natural logarithms?

There are so many available bases. Why is the strange number $e$ preferred over all else? Of course one could integrate $\frac{1}x$ and see this. But is there more to the story?
15
votes
3answers
2k views

Why is Euler's number used as a base for logarithms? [duplicate]

Is there some special property of '$e$' which makes it suitable to be used as a base for logarithms? Moreover, does the natural logarithm possess some advantage over the common logarithm? I don't ...
0
votes
2answers
2k views

Find Log equation from data points

I have the following data points, (left hand column goes from 0-127, right hand column goes from 30-22000 hz. Is there any calculator I can use to find a "log" function of this data, so that it comes ...
-5
votes
0answers
21 views

Limits with exponential functions [on hold]

First prob: ( I tried with $e^{\ln}$ property but doesn't work) Here is the first problem pic Second prob:(at this if I get stuck at the part where I got $\frac{e^1}{x^2} - \frac{e^1}{x^2}$) second ...
0
votes
2answers
18 views

Solving equation of form $x = -a/ln(bx)$

I have an equation that I am trying to solve, which can be reduced to the form $$ x = -\frac{a}{\ln(bx)}$$ where I am trying to solve for $x$. Mathematica says the solution is of the form $$x = ...
0
votes
3answers
20 views

Need to overcome erroneous result when differentiating natural log of a fraction

I am trying to differentiate the following: $$ln(3x-8/6x+2)$$ my (incorrect) method is: let $$ln(x) = ln(u)$$ therefore when differentiating u.. $$ln(u) = 1/u$$ and diff of$$$$(3x-8/6x+2) = 3/6 = ...
2
votes
2answers
39 views

Evaluate $\lim_{x\rightarrow\infty} \ln(x^2+1)-\ln(x-1)$

How would you solve the following limit? The method I used can be seen below. I'm just not sure if it's valid. I was thinking perhaps a substitution for $(x-1)$ might also work, but when I followed ...
0
votes
1answer
23 views

Algebra, rewriting a formula

I have to rewrite this formula: $$10^{-5,6-0,4m}=\frac{c}{x^2}$$ To: $$m(x)= -14,0-2,5logc + 5,0logx$$ But im stuck at: $$m(x)= \frac{2logx -logc+5,6}{-0,4}$$ and have no idea how to continue from ...
0
votes
1answer
27 views

Question regarding integration of $ln(f(x)^{g(x)})$

I am trying to solve the following integral: $$\int ln[(x+2)^{x+5}] dx$$ I'm not entirely sure how to go about this. Since I know that $\int udv = uv - \int vdu$ I started by assigning $u = ...
0
votes
0answers
6 views

Equation of semilog line

I am trying to determine the equation for a line passing through points (10, 0.5) and (100,0.3) where the x axis is on a logarithmic scale and the y axis is on a regular scale. This should be simple ...
1
vote
0answers
19 views

Issue an integral involving a $\log$

Let $$F(t)=\frac{t+7}{2+t}$$ and $$E(t)=\frac{\ln(t+4)}{t+2}\,.$$ My job is to compute the area between them from $x=0$ to $x=5$, which got me from $$\int_0^5{F(t)-E(t)}$$ to ...
1
vote
1answer
40 views

Natural Logs and Anit-Derivatives are kicking me

I am given a problem involving rates of flow, $F(t)=\frac{t+7}{2+t}$ is the rate at which a bucket is being filled. The same bucket is being emptied at a rate given by $E(t)=\frac{\ln(t+4)}{t+2}$. My ...
3
votes
3answers
72 views

Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$

I was given a task to prove that inequality is true for x>0: $(e^x-1)\ln(1+x) > x^2$. I've tried to use derivatives to show that the $f(x) = (e^x-1)\ln(1+x)-x^2$ is greater than zero, but has never ...
3
votes
3answers
32 views

Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$

How do I show that $\ln(x) = \lim_{n\to\infty} n (x^{1/n} - 1)$? I ran into this identity on this stackoverflow question. I haven't been able to find any proof online and my efforts to get from ...
1
vote
1answer
124 views

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 ...
0
votes
1answer
11 views

Formula for calculating markup with big % for small amounts and small % for larger amounts

I am trying to come up with a formula for calculating markup for products that range in value from a few cents up to tens of Dollars. At 10c I would like the markup to be around 500%, and from 2 ...
4
votes
3answers
141 views

Prove that $f(ab) = f(a) + f(b)$

Question : Assume only that $f: (0,\infty)\to{\mathbb{R}}$ is differentiable and that $f'(x) = 1/x$, and $f(1)=0$. Prove that for all $a,b \in(0,\infty)$, $f(ab)=f(a)+f(b)$. [Hint: Let $g(x)=f(ax)$] ...
5
votes
3answers
253 views

Proving $x$ is a given quotient of logarithms

I'm practicing some questions on logarithms at the moment in order that I'm up to speed with the problem solving aspect before I embark on my PHD in chemical engineering at Boston college next year. ...
1
vote
5answers
47 views

Multiplying two logarithms (Solved)

I was wondering how one would multiply two logarithms together? Say, for example, that I had: $$\log x·\log 2x < 0$$ How would one solve this? And if it weren't possible, what would its domain ...
0
votes
1answer
12 views

Exhaustive search times: 2 to power k = 100 hours - double k, how many hours

An exhaustive search (i.e. checking all combinations of values) takes 100 hours to go through all permutations where a binary key has a length of k. $2^k$ = 100 hours where k is the number of digits ...
0
votes
0answers
25 views

log(x,2log(2x, 2log(2,4x))) >1 , find answers of x

how i slove it , please help me? log(x,2log(2x, 2log(2,4x))) >1 my try: if x>1 =>2log(2x, 2log(2,4x))>x => 2log(2,4x)>(2x)^(x/2) =>4x>2^(((2x)^(x/2))/2) another way log(x,2log(2x, ...
11
votes
1answer
67 views

If $\log_35=a$ and $\log_54=b$, what is $\log_{60}70$?

One student sent me this question: If $\log_35=a$ and $\log_54=b$, what is $\log_{60}70$? Question asks the value of $\log_{60}70$ in terms of $a$ and $b$. Equations for $a$ and $b$ involved ...
10
votes
5answers
138 views

How do you solve $x^2 = \left(\frac 12\right)^x $?

I'm having trouble finding the steps to solve for $x$. The solutions to this equation are $x=-4$, $x=-2$, and $x=0.76666$ when solved graphically and through the solve function of a TI-nspire cx CAS. ...
10
votes
3answers
408 views

Number system with $e^x = 0$ for some $x$

It is well known that $e^x \ne 0$ for all $x \in \mathbb{R}$ as well as $x \in \mathbb{C}$. Upon reading this article and doing a bit of research I have found that this also applies to the ...
1
vote
2answers
23 views

Cancelling a logarithm

I was wondering if there was a way to cancel out a logarithm? For example: $\log_a A$ > $\log_a B$ What would a have to be for the log to go away and be left with A > B? Thanks in advance!
1
vote
2answers
38 views

So many logs with different bases

$ \large { 6 }^{ \log _{ 5 }{ x } }\log _{ 3 }( { x }^{ 5 } ) -{ 5 }^{ \log _{ 6 }{ 6x } }\log _{ 3 }{ \frac { x }{ 3 } } ={ 6 }^{ \log _{ 5 }{ 5x } }-{ 5 }^{ \log _{ 6 }{ x } }$ The sum of ...
0
votes
1answer
19 views

Find unknown x coordinate from log graph

I am not sure where to start on this question. I am not sure how to fit the coordinates into the equation $y=\log_3(x-4)$
1
vote
1answer
39 views

How to prove derivative of logarithm with base $b$?

I learned how to derive a logarithm with any base. This is the formula: $$\frac{d}{dx}\log_bx=\frac{1}{x\ln b}$$ How can it be proved?
2
votes
1answer
90 views

How $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots =\ln 2$? [duplicate]

while doing the Integration problem using Limit of a sum approach i have a doubt how $$1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots =\ln2$$ by infinite geometric series we have ...
0
votes
2answers
66 views

If the integral of $c/x$ is $c.log(x)+C$ what is the base?

This question is a follow up to an answer I gave here: How to integrate $1/x$? After the algebra I said that 'This step of course gives the argument of $ln()$ the value $e$ and note that so far we ...
0
votes
2answers
32 views

what is the series for determining an unknown exponent [closed]

Embarrassing... I don't remember what series I would use to solve for $x$ in a simple equation such as the following: $4^x=7$ (aka $x=\log_4 7$) Thanks in advance, Alan UPDATE: I'm asking what ...
5
votes
3answers
491 views

How much proof is needed in such paper (Maths related)?

I'm writing a paper (report) regarding Euler's Number $\space e \space$ (even though he didn't discover it). Within this paper, I show that: $${d\over dx} {e^x} = {e^x}$$ **NOTE: ** This is not ...
0
votes
1answer
84 views

Logarithm in the exponent

$$(2x)^{\log 2} = (3y)^{\log 3} \\ 3^{\log x} = 2^{\log y}$$ Solve for $x$ and $y$. My intuition for solving such problems is taking the logarithm on both sides but it does not work. I also ...
0
votes
1answer
28 views

What is the value of $x$ in this logarithmic inequality? [closed]

Please help me with this inequality : $$\log_2 (x^2-2x) - 3 >0 $$
1
vote
2answers
40 views

Logarithm question with base change

If $\log_{12} 27 = a$ then find the value of $\log_6 16$.
15
votes
6answers
9k views

Calculate logarithms by hand

I'm thinking of making a table of logarithms ranging from 100-999 with 5 significant digits. By pen and paper that is. I'm doing this old school. What first came to mind was to use $\log(ab) = ...
0
votes
1answer
14 views

Calculating the amount of times a binary search could run (worse case) without a calculator/calculating base 2 logs without a calculator.

Ok so I had a question on a test that I had to do without a calculator. And I can not figure out how in the world I am supposed to do it without a calculator. The question asked to find how many ...
-2
votes
3answers
57 views

Can someone please explain how $60+\ln(64)-\ln(8)$ is equal to $60+\ln(8)$ [closed]

Can someone please explain how $60+ \ln(64)- \ln(8)$ is equal to $60+\ln(8)$. I can't understand why this is true.
1
vote
1answer
30 views

Solve $\log_9(x-4) - \log_9(x-8)= \frac{1}2$

Solve $\log_9(x-4) - \log_9(x-8)= \frac{1}2$ $(x-4) - (x-8)= 9^\frac{1}2$ $(x-4) - (x-8)= 3$ The answer is 10 but I am not sure how that was obtained.
0
votes
2answers
44 views

what is the value of $x$ in this logarithmic question? [closed]

What is the value of $x$: \begin{equation} x^{\log_5 x} >5 \end{equation} Thanks for the help.
0
votes
3answers
52 views

Is $n^\frac{1}{10} \in O((\log n)^{10})$?

This question came up in a recent discussion: is $n^\frac{1}{10} \in O((\log n)^{10})$? First time I've come across a power of a log in a long time, and as far as I recall, there are no identities ...