# logarithm

2. ### Some limits manipulation.

Could someone explain the steps involved in this limit? I'm reading a proof and kinda stuck here. For k \in \mathbb{Z}^+ and c a positive constant, set \beta_k = c \sqrt{\frac{k}{\ln(k)}} and \delta_k = \frac{\ln(\frac{k}{\beta_k})}{k}. Then \lim\limits_{k \to \infty} (\beta_k(1-\delta_k)^k +...

4. ### Logarithm, Gamma and Brain Failures

Can someone explain the difference between $$\ln\Gamma(z)$$ and $$\ln(\Gamma(z))$$ Here is WolframAlpha link : https://www.wolframalpha.com/input/?i=integrate+ln%28Gamma%28z%29%29
5. ### pH logarithm

Hello I am quite confused about a question I have got on a test. I was wondering if I can get some help since I have looked online and it doesnâ€™t seem to fit with my question which confuses me. In my lesson it states that a value of 2(log10 100) is ten times greater than a value of 1(log10...
6. ### Logarithm binary numbers

Hello everyone, I am currently learning about binary numbers and I have stumbled on this problem: "write a function (log n) that calculates the logarithm (base 2) of number n. Number n is a positive binary number". (only using binary arithmetic operations) I know this is a very basic question...
7. ### Proof for natural logarithm limit without differentiation

I have another limit where I'm struggling with the solving.Can somone help me? https://ibb.co/5Kq58jR I used a method like this but I'm not 100% if it's correct! https://ibb.co/JQrpdL1 What should I do from that step? I know something like arctan(x)/x when x tends to 0 is 1. How is that...
8. ### Prove the limit of natural logarithm without differentiation or Taylor series

Can someone help me to prove that this limit is equal to 1 without using differentiation or Taylor Series?(like in the limit of sinx/x when x tends to 0)What are the steps? https://imgur.com/a/WslKnLI

No clue on where to start.

11. ### Logarithm

Given log2=0.69, log3=1.10 and log7=1.90, all to a fixed base, find log10.5 without using table.
12. ### How to find logarithm of a number having negative characteristic.

Hi, can anybody help me find logarithm of a number having negative characteristic? For example, log(0.00462). Any help would be highly appreciated. Thanks.
13. ### Inequality with an abs. value, exponent and logarithm

This given problem is $x^\left|\log_xa\right|\leq\frac{1}{a}$ with the following solution sets: $x\in(0,1)\cup(1,+\infty),\ a\in(0,1]\\ x\in(0,1),\ a\in(1,+\infty)$ This is how I've approached it: \$\left|\log_xa\right|=\left\{\begin{aligned}\log_x&a\left\{\begin{aligned}x>1\ &\land\ a\geq...
14. ### Logarithm

Hi, I don't understand how 0.1 x become 10 here: log2 (50/3) = 0.1x = 10 X log2 (50/3) Here they don't do that https://www.wolframalpha.com/input/?i=log2+(50%2F3)+%3D+0.1x Thank in advance.
15. ### Logarithm Calculations Help

I'm a university student and still can't do calculations with logarithms :( i'm trying to calculate this: log8(4) <=> 8^x = 4 but i can't find x!!! I mean how can u multiply 8, x times with itself and find 4!!! This is insane!!! This made me think something that i never thought about all...
16. ### Logarithm syntax what does ^3log(27) mean?

From my exercise book the book wants me to calculate \displaystyle ^3\log 27, but I don't know what this syntax means? Is it the same as \displaystyle \log_3 27?
17. ### logarithm

Is logarithm a arithmetic operation?
18. ### Which Forum ?

Greetings to all - This is my first time here. I registered because I have a question about how to enter a logarithm, raised to a power of -1, on my brand new TI-84 Plus calculator. Any suggestions for the appropriate forum? Many Thanks !:o
19. ### Two ways to integrate

Integrate with respect to x: _____14_____ + 7 exp^(14x/5)-1 I got (through intg by substitution multiple times): 7x + 5log(modulus( 1 - exp^(-14x/5) )) but because I need the definite integral over (0, b), subbing in 0 gives an undefined integral On integral-calculator and...
20. ### Logarithm function

Hi, If*log10(b)=1.8*and*loga(b)=2.5752, what is*a? How does the change of base rule apply here when there are two unknowns a & B ? Thanks, amphi