Build Your Logarithms Skills with Engaging Lessons and Exercises

Classify the equation 7^log base 7 power x

Kassandra Cherry 2022-03-17

A rigid exponential question
This question was given by my friend
$x^{x^{20}} = 2 - \sqrt[\sqrt{2}]{2}$

Joey Rodgers 2022-03-17

Closed form for $\sum_{n = 1}^{\infty} \frac{\cos (π \log n)}{n^{2}}$

Kayden Chandler 2022-03-16

Any tricky method to solve this one?
The question : Prove that :
$if y = 2 x^{2} - 1, then [\frac{1}{y} + \frac{1}{3 y^{3}} + \frac{1}{5 y^{5}} + \dots]$
is equal to
$\frac{1}{2} [\frac{1}{x^{2}} + \frac{1}{2 x^{4}} + \frac{1}{3 x^{6}} + \dots]$
Here I have modified the question, in the actual question (from my paper) there were four other options given,my approach was to reduce the first expression to $\frac{1}{2} \ln (\frac{y + 1}{y - 1})$ and then trying to check for each options to find the match, now is there any other approach for this one ? Since it took me sometime for checking each options :( and the desired answer is at the last option!

kinkonillohup 2022-03-16

What is the limit of multiple logarithm quotient $\frac{\log_{2} (\log_{2} (n))}{\log_{2} (n)}$
Could somebody check if this is correct?
$lim_{n \to \infty} \frac{\log_{2} (\log_{2} (n))}{\log_{2} (n)}$
I exponantiate the numerator and the denominator with 2
$\frac{{(\log_{2} (\log_{2} (n)))}^{2}}{{(\log_{2} (n))}^{2}}$
$= \frac{\log_{2} (n)}{n}$
I extract the constant from the logarithm
$= \log_{2} (e) \cdot lim_{n \to \infty} \frac{\ln (n)}{n}$
Using de l'Hospital:
$= \log_{2} (e) \cdot lim_{n \to \infty} \frac{\frac{1}{n}}{1}$
$= \log_{2} (e) \cdot lim_{n \to \infty} \frac{1}{n} = 0$
Is that correct?

Thalia Ortiz 2022-03-16

Comparing rates of change: which function increases faster?
I am comparing two functions for $x \geq 1$
$f (x) = \ln (⌊ \frac{x}{9} ⌋!) - \ln (⌊ \frac{x}{10} ⌋!) - \ln (⌊ \frac{x}{90} ⌋!)$
$g (x) = (2.07766) \sqrt{\frac{x}{9}} + (0.057712778) x$
Comparing their values over a finite range suggests that f(x) grows slightly faster than g(x).
Since f(x) is not continuous, I am not able to use its derivative to establish the rate of growth. How can I verify that as x increases, f(x) increases faster than g(x)?
It looks like I copied the problem wrong. It should have read $(0.057712778) x$ instead of $(0.103883) x$ . The correct term was $(1.03883) \cdot \frac{x}{18} = (0.057712778) x$

Damian Hanna 2022-03-16

Calculating how long it will take for the half-life of X amount to fall below Y amount
I am trying to determine how long it will take $(t)$ for the half life of 500 amount of substance to fall below 100 (to be $\leq 99$ -- I am only concerned with integers) when it has a half life of 5.
I have gotten this far in the calculation:
$99 = 500 {(\frac{1}{2})}^{\frac{t}{5}}$
So I guess my questions are as follows:
1.Have I set this up right?
2.Is there a better way to do this?
3.Can somebody point me in the direction of how to solve from here?

Babolkybya 2022-03-15

Arithmetically showing that $\frac{\log (x + 1)}{\log (x)} < \frac{x + 1}{x}$
Is there a possibility that this can be shown arithmetically? By arithmetically, I mean not looking at the graph.
$\frac{\log (x + 1)}{\log (x)} < \frac{x + 1}{x}$
Thank You

Jerimiah Hansen 2022-03-15

Approximating a simple sum
Can somone help me find an assymptotic formula for n, for fixed x , for this sum , perhaps an inequality would be even better, or some bound on the error.
$\sum_{k = 1}^{n} \frac{1}{\log (k x)}$
I need somthing better then the integral from 1 to n of ln(kx) with respect to k. Its also okay if you use special functions, like the logarithmic integral.

Caroline Carey 2022-03-14

What is the value of integral $\ln x$ ? Example:
$\int_{2}^{4} (5 x^{4} + 2 x + 5 + 2 \ln x + \frac{1}{x}) d x$

arrostetzwyl 2022-03-14

Why is $2 \ln (662 + π)$ so close to $13$ ?

Ben Shaffer 2022-03-13

What will the value of following log expression
$\log_{x} \frac{x}{y} + \log_{y} \frac{y}{x}$
I tried: $\log_{x} x - \log_{x} y + \log_{y} y - \log_{y} x = 1 - \log_{x} y + 1 - \log_{y} x = 2 - \log_{x} y - \log_{y} x$
Now what after this ?

Abbie Edwards 2022-03-12

What is the simple way to show that
$\frac{N \log {N}}{k \log {k}} \approx \log_{k!} {N!}$
I tried to use the factorial and the log rules but..
Thanks.

Charity Odom 2022-03-12

What is wrong with this solution?
$\ln (x) = 1 + \ln (5)$
$x = e^{1 + \ln (5)} = e^{1 + 5} = e^{6}$
What exactly am I doing wrong here?

Payton Benson 2022-03-09

Write $\log_{218} x^{2} y^{5^{2}}$ as a sum of logarithms. Express powers as factors.

Neatlyvat91g 2022-03-09

why $\log (n!)$ isn't zero?
I have wondered that why the $\log (n!)$ isn't zero for $n \in N$
Because I think that $\log (1)$ is zero so all following numbers after multiplying the result will become zero.
Thanks in advance.

Ezra Phillips 2022-03-09

Without using logarithms, solve for x in terms of y. Show all steps.
$4^{x - 1} = 16^{2 y}$

Roman Case 2022-03-08

Write each expression as a sum and/or difference of logarithms. Express powers as factors.
1. $\log_{5} (25 x)$
2. $\log_{3} \frac{x}{9}$

chechemua62l 2022-03-08

Write each expression as the sum and/or difference of logarithms.Express powers as factors.
$\log_{5} (\frac{x^{2} + 2 x + 1}{x^{2}}), x > 0$

nevinijifg8 2022-03-07

Write each expression as a sum and/or difference of logarithms.Express powers as factors.
$\ln \frac{5 x \sqrt{1 + 3 x}}{{(x - 4)}^{3}}, x > 4$

Finding logarithms questions and answers online is always pure luck, especially if these are provided with detailed answers to questions. This is exactly what you can find below regardless of your practical application, college course, or complexity. These logarithms questions are related to higher education courses, which is why they will help you find the answers to what you currently have. When you deal with logarithmic equations you are approaching an exponential equation where the variable appears in an exponent as it’s in (log b (bx) = x. It also shows that the logarithmic graph equation can be represented as well.

Algebra II

Learn How to Graph Logarithmic Equations