Build Your Logarithms Skills with Engaging Lessons and Exercises

Working with logarithms
I have an expression involving very small probabilities $A, B, C, D .$
$x \geq \frac{k_{1} B}{A + k_{2} B}$
$x \leq \frac{k_{1} C}{D + k_{2} C}$
Is there any way for me to check if x satisfies the above inequalities using $\log (A), \log (B), \log (C)$ and $\log (D)$ ?

e3r6a2n1dz60 2022-03-06

Yet another logarithm multiplication doubt
I'm here again, now with a doubt on multiplication on logarithms, I have the expression: $(\log_{5} 2 + \log_{5} 3 \cdot \log_{3} 4) \cdot \log_{2} 5$
I've evaluated it to:
$(\log_{5} 6 \cdot \frac{\log_{5} 4}{\log_{5} 3}) \cdot \frac{1}{\log_{5} 2}$
What should I do with this multiplications ?
EDIT: So, I failed miserably on algebra through, so I evaluated now to:
$= (\log_{5} 2 + \log 5 4) \cdot \log_{2} 5$
$= (\log_{5} 8) \cdot \frac{1}{\log + 52}$
$= \log_{5} (\frac{8}{2})$
$= \log_{5} 4$
So, do I solved it correctly now ? Thank you. EDIT 2:
$= (\log_{5} 2 + \log_{5} 4) \cdot \log_{2} 5$
$= (\log_{5} 8) \cdot \frac{1}{\log_{5} 2}$
$= \frac{\log_{5} 8}{\log_{5} 2}$
$= \log_{2} 8 = 3$

Kelsie Cantu 2022-02-12

Use the properties of logarithms to expand the following expression as much as possible. Simplify any numerical expressions that can be evaluated without a calculator.
log5(125x+75y)

Gideon Oliver 2022-02-12

Find the dimension of fractal with a scaling ratio of r=3 and a replacement ratio of N=11. Round you answer to the nearest hundredth

derlingasmh 2022-01-23

How to formally show that $f (z)$ is analytic at $z = 0$ ?
Let $z$ be a complex number. Let
$f (z) = \frac{1}{\frac{1}{z} + \ln (\frac{1}{z})} .$
How to formally show that $f (z)$ is analytic at $z = 0$ ? I know that for small z we have
$| \frac{1}{z} | > | \ln (\frac{1}{z}) |$
and that implies $| f (0) | = 0$ . Are there multiple ways to handle this ?

Fallbasiss4 2022-01-23

The differential for each function can be found:
$(a) y = x^{2} \sin (4 x)$
$d y =$
$(b) y = \ln (\sqrt{(1 + t^{2})})$
$d y =$

Celia Horne 2022-01-23

Evaluate $lim_{y \to 0} \frac{\log (1 + y)}{y}$ without LHR or Taylor series

Vanessa Hensley 2022-01-23

Logarithmic Series Evaluation
I was trying to generate a direct formula for this series but I am not sure whether it is possible to do so.
$1 \ln (1) + 2 \ln (2) + 3 \ln (3) + 4 \ln (4) + \dots + (n - 1) \ln (n - 1) + n \ln (n)$

Turnseeuw 2022-01-23

Prove
$\frac{1}{x + 1} < \ln (\frac{x + 1}{x}) < 0.5 (\frac{1}{x} + \frac{1}{x + 1})$

m4tx45w 2022-01-23

Why cant

Laney Spears 2022-01-22

Find $n$ satisfying the equation $[\log_{21}] + [\log_{22}] + [\log_{23}] + \dots [\log_{2} n] = 1538$

socorraob 2022-01-22

Are logarithms the only continuous function on $(0, \infty)$ such that $f (x y) = f (x) + f (y)$ ?

taoigas 2022-01-22

A closed form for $\int_{0}^{1} \frac{\ln (- \ln x) l i^{2} x}{x} d x$

David Lewis 2022-01-22

Solve $- B \ln y - A y \ln y + A y - A = 0$ for $y$

fanyattehedzg 2022-01-22

Information on the sum $\sum_{n = 1}^{\infty} = \frac{\log n}{n!}$

PEEWSRIGWETRYqx 2022-01-22

How do I show this inequality that
$\frac{\ln (x + 1)}{\ln (x)} \leq \frac{x}{x - 1}$ for $x > 1$ ?

untchick04tm 2022-01-22

How to solve the following logarithmic equation: $n (n - 1) 3^{n} = 91854$

Ernest Ryland 2022-01-22

Infinite sum of logs puzzle
Here is a neat infinite sum puzzle:
Prove the following is true when $| x | < 1$
$- \ln (1 - x) = \ln (1 + x) + \ln (1 + x^{2}) + \ln (1 + x^{4}) \dots \ln (1 + x^{2 k}) \dots$
$- \ln (1 - x) = \sum_{k = 0}^{\infty} \ln (1 + x^{2 k})$

Margie Marx 2022-01-22

Derive $\log (a + b) = \log (a) - 2 \log (\cos (\arctan (\sqrt{\frac{b}{a}})))$

Sapewa 2022-01-22

How can I solve $8 n^{2} = 64 n \log_{2} (n)$

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