Build Your Logarithms Skills with Engaging Lessons and Exercises

if $m = \log_{10} n$ , what other relationship exists between m, 10, and n?

etudiante9c2 2022-04-24

how to find the value of $\log_{37}$

airesex2 2022-04-24

How to derive the following series expansion for $\ln (\frac{x + 1}{x - 1})$
How to prove :
$\ln (\frac{x + 1}{x - 1}) = 2 [\frac{1}{x} + \frac{1}{3 x^{3}} + \frac{1}{5 x^{5}} + \dots]$
where $| x | > 1$
I am not able to get how to proceed on this one ?

Treboldiqtw 2022-04-23

In a and b, solve for x.
a) $\log x = 5$
b) $\log x = 1.25$

vacinammo288 2022-04-23

If I knew that by the year 2000 that there were 1 trillion humans, and that they started reproducing 2000 years before that, how would I calculate their birth rate?
Assume an initial population of 1 million, and a reproduction age of 15.
Also take into account a standard death rate, where death occurs after 75 years, and reproduction age ends at 50.
Assume a uniform age distribution.

Averie Ray 2022-04-23

How should I calculate the Lebesgue integral of logarithm function from zero to infinity?
Does the area under the $\ln (x)$ in $(0, + \infty)$ is measurable? If yes, how can I calculate it?

Gage Potter 2022-04-23

How does this simplify to $\log \sqrt{x}$
How does $\log x - \log \sqrt{3} x - \log \sqrt{6} x$ simplify to $\log \sqrt{x}$
I've tried to get Bagatrix Algebra Solved! to solve it, but it even got the wrong answer... (I checked it by replacing x with 5 and typing it out on a calculator..)
No matter what I do, I end up with an answer that is correct and a bit simplified, but not as simplified as $\log \sqrt{x}$

Rylan Sullivan 2022-04-23

How to calculate the integral
$I = \int_{0}^{1} \frac{x^{n} - 1}{\ln (x)} d x$

kadetskihykw 2022-04-22

Solving a logarithmic equation
$\ln (x + 1) = 2 + \ln (x - 1)$ ; solve for x.
From there I get
$\ln \frac{x + 1}{x - 1} = 2 .$

estrigaslju 2022-04-22

Solve in terms of b:
$\log_{b} (1 - 3 x) = 3 + \log_{b} x$

yert21trey123z7 2022-04-22

Solve a simple equation with log in it
I'm stuck with solving this equation,
$2 \log x = \log 9$
This is how far I made it:
$\log x = \log 4, 5$
$x = ?$ I'm a beginner at logarithms so I appreciate ways to solve it and not just an answer.

nrgiizr0ib6 2022-04-21

How to compute the asymptotic growth of $(\begin{matrix} n \\ \log n \end{matrix})$ ?

kulisamilhh 2022-04-20

How to find the limit of $\frac{\ln (\ln (\frac{n}{n - 1}))}{\ln (n)}$ ?
How do you find
$lim_{n \to \infty} \frac{\ln (\ln (\frac{n}{n - 1}))}{\ln (n)}$
I know it's -1, but I had to plot it.

eszkortwxp 2022-04-20

Solving
$\log_{2} (x - 4) + \log_{2} (x + 2) = 4$
Here is how I have worked it out so far:
$\log_{2} (x - 4) + \log (x + 2) = 4$
$\log_{2} ((x - 4) (x + 2)) = 4$
$(x - 4) (x + 2) = 2^{4}$
$(x - 4) (x + 2) = 16$
How do I proceed from here?
$x^{2} + 2 x - 8 = 16$
$x^{2} + 2 x = 24$
$x (x + 2) = 24$ Which I know is not the right answer
$x^{2} + 2 x - 24 = 0$ Can't factor this

Halle Marsh 2022-04-20

Solve ${(\log_{3} x)}^{2} + \log_{3} (x^{2}) + 1 = 0$

Hugh Walls 2022-04-20

Solve
$\log x + \log (2 x - 5) = \log 96 - \log 8$
I started by doing this:
$\log 2 x^{2} - 5 x = \log 12$
Then I got rid of the logs. Can I do that?
$2 x^{2} - 5 x = 12$
What do I do next? What is x?

Molecca89g 2022-04-19

Solve for x: question on logarithms.
The question:
$\log_{3} x \cdot \log_{4} x \cdot \log_{5} x = \log_{3} x \cdot \log_{4} x \cdot \log_{5} x \cdot \log_{5} x \cdot \log_{4} x \cdot \log_{3} x$
My mother who's a math teacher was asked this by one of her students, and she can't quite figure it out. Anyone got any ideas?

painter555ui8n 2022-04-18

How do I solve for V in this equation?
$\frac{\ln (T + 1) - \ln (V - S + 1)}{\ln (V - S + 1)} = \frac{1}{K} - 1$
What are the steps if I want to solve for V?

Bryanna Leon 2022-04-16

Is $\log_{23} > \log_{35}$ ?

Camila Glenn 2022-04-16

What is $\frac{d y}{d x}$ of a square root using logarithmic differentiation?
I thought I knew how to do logarithmic differentiation until I came across this:
$y = \sqrt{x (x + 7)}$ find dy/dx by logarithmic differentiation
I was not phased by the problem and did the following work:
$\ln (y) = \ln (\sqrt{x (x + 7)})$
$\ln (y) = \frac{1}{2} (\ln (x) + \ln (x + 7))$
$\frac{1}{y} \frac{d y}{d x} = \frac{1}{2} (\frac{1}{x} + \frac{1}{x + 7})$
$\frac{d y}{d x} = \frac{y}{2} (\frac{2 x + 7}{x^{2} + 7 x})$
but then found out that that was not actually what the answer was if you take dy/dx without logarithmic differentiation. What am I doing wrong? I have spent the past hour trying to figure it out with no luck.

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