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Simple log inequality (CAL 1)
I am an amateur when it comes to math. I am currently taking CAL 1 and have a question about one of my assignments. Any help is appreciated.
Let $g (x) = x^{3} - x^{3} - 2 x$ and $f (x) = \ln (g (x))$ I have to find the domain of $y = f (x)$ I've figured out that when I do $x^{3} - x^{2} - 2 x > 0$ I end up with $0, 2, - 1 .$
But I'm still not sure what the domain is.... maybe I'm close? maybe it's obvious? Any help much appreciated!!!
Thanks.

Gage Potter 2022-04-30

Problems with the number 0
Here is the original formula:
$\frac{256}{2^{x}} = y$
In order to solve for x, I've done this:
$\log_{2} (\frac{256}{y}) = x$
The problem is that y can be zero. What should I do to solve for x?

Dereon Guzman 2022-04-29

Limit $lim_{x \Rightarrow \infty} x - x^{2} \ln (1 + \frac{1}{x})$

broggesy9 2022-04-28

Product rule for logarithms works on any non-zero value?
The product rule for logarithms states that:
$\log_{b} M + \log_{b} N = \log_{b} (M \cdot N)$
Most sources that I've found* state that this rule only applies when M and N are positive. It's true that $\log_{b} 0$ is undefined, but negative values in place of M and N seem to work just fine:
$\log (- 1) + \log (4) = \log (- 1 \cdot 4)$
Why the discrepancy?

Kaiya Hardin 2022-04-28

Is it standard to say $- i \log (- 1)$ is $π$ ?

veleumnihryz 2022-04-28

Simplify expression using the properties of logarithms.
$3 \log_{4} r^{2} - 2 \log_{4} r$

livinglife100s8x 2022-04-27

If $x = \log_{12} 27$ ,then what is the the value of $\log_{616}$ ?

diasenamorn5l 2022-04-27

Way to calculate exponent in congruent equation
I want to solve
$5^{x} \equiv 21 (mod 23)$
Is there a way to get the $x$ without trial & error?

Maurice Maldonado 2022-04-27

Solution for $\log_{7} x + \log_{\frac{1}{7}} x^{2} = \log_{49} x - 3$

Jaidyn Cook 2022-04-26

How to determine $lim_{n \to \infty} n \ln (1 + \frac{1}{n})$

tefoldaavv 2022-04-26

How $a^{\log_{b} x} = x^{\log_{b} a}$

Deven Livingston 2022-04-26

What is intresting about
$\sqrt{\log_{x} \exp \sqrt{\log_{x} \exp \sqrt{\log_{x} \exp \dots}}} = \log_{x} e$
Why does
$\sqrt{\log_{x} \exp \sqrt{\log_{x} \exp \sqrt{\log_{x} \exp \dots}}} = \log_{x} e = \frac{1}{\ln x}$
There only seems to be a relation when using square roots, but not for cubed roots or anything else. Why does this equation work and why does it only work for square roots?
(The $e$ is not significant, by the way. You could give the exponential function a different base, $a$ , and say the equation equals $\log_{x} a)$ .

Bronson Olson 2022-04-26

What is solution of this equation
I am new to logarithms, I am confused what to do when any constant is raised to a power such as $1 + \log x$ .
As in this equation, $9^{1 + \log x} - 3^{1 + \log x} - 210 = 0$
While I try to take log on both sides, things get messy.
All the logs have base 3.

dolovatgyp 2022-04-26

Simplify expression using the properties of logarithms
$\log_{53} k + \log_{57} k^{3}$

caldaridvq 2022-04-26

simplify natural logarithm
How to simplify this natural logarithm
$\frac{1}{2} \ln | y + 1 | - \frac{1}{2} \ln | y - 1 | + \ln | C | = \frac{1}{2} \ln | x + 1 | - \frac{1}{2} \ln | x - 1 |$
if I apply the logarithm rule
$\ln \sqrt{| y + 1 |} - \ln \sqrt{| y - 1 |} + \frac{1}{2} \ln (C^{2}) = \ln \sqrt{| x + 1 |} - \ln \sqrt{| x - 1 |}$
Please help further..

redupticslaz 2022-04-25

How can I show that $lim_{x \to \infty} \frac{\log (x + 1)}{\log x} = 1 ?$

Gage Potter 2022-04-25

Using laws of logarithms, write the expression in the image as a single logarithm.
$6 \log (64 - x^{2}) - (\log (8 + x) + \log (8 - x) = \log ()$

zergingk8l 2022-04-25

Simplifying Logarithmic Expression
Compute:
$\frac{1 - \log_{a}^{3} b}{(\log_{a} b + \log_{b} a + 1) \log_{a} \frac{a}{b}}$
I tried to expand it :
$\frac{1 - \log_{a}^{3} b}{(\log_{a} b + \log_{b} a + 1) \log_{a} \frac{a}{b}}$
$= \frac{(1 - \log_{a} b) (\log_{a}^{2} b + \log_{a} b + 1)}{(\log_{a} b + \log_{b} a + 1) (1 - \log_{a} b)}$
$= \frac{(\log_{a}^{2} b + \log_{a} b + 1)}{(\log_{a} b + \log_{b} a + 1)}$
But I got nothing.

Deven Livingston 2022-04-25

Simplify log expression with infinite series $\log x - \sum_{{i = 1}}^{\infty} \frac{x^{i}}{i}$

Molecca89g 2022-04-24

Natural log summation representation
In working through a problem, I've encountered the need to express
$\log n = \sum_{k = 1}^{n - 1} \log (1 + \frac{1}{k})$
where $\log k$ is the natural logarithm of k. I'm fairly certain the above equality holds (please let me know if otherwise), but I'm not quite sure how to derive it. Any help would be greatly appreciated.
So far, I've tried expressing $\log n = \log (n!) - \log ((n - 1)!)$ to no avail.
Many thanks!

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