Build Your Logarithms Skills with Engaging Lessons and Exercises

Integral of $\int \frac{1}{\log x} d x$

Franco Franco 2022-01-22

Proving or disproving: If $0 < a < b < 1$ , then ${(1 - a)}^{b} > {(1 - b)}^{a}$

Aaden Lam 2022-01-22

Comparing Powers of Different Bases
How can I know if one power is bigger than the other when the bases are different?
For example, considering $2^{10}$ and $10^{3}$ the former is the greater one, but how to prove this? Logarithms? I'll be working with big numbers, and though a more general solution is really appreciated, I will be comparing exactly powers of $2$ and $10$ .

Abbie Mcgrath 2022-01-22

If x is rational, can $\frac{\log (1 - x)}{\log x}$ be algebraic?

iocasq4 2022-01-22

Use the unique factorization for integers theorem and the definition of logarithm to prove that $\log_{3} (7)$ is irrational.

Gwendolyn Giles 2022-01-22

Simple algebra clarification needed for Gaussian entropy formula
Norwich (2003) gives the following equality based on a substitution
$H = \frac{1}{2} \ln (2 π σ^{2}) + \frac{1}{2}$

Anika Osborne 2022-01-22

Break up the following function using laws of logarithms, then compute the derivative. $f (x) = \ln (\frac{6 (x + 1)}{x^{3}})$

Rudy Koch 2022-01-22

Express $\ln x y^{2}$ as a sum, difference or multiple of logarithms.

Yahir Haas 2022-01-22

Prove that
$- 2 \log (2) = - 2 + \sum_{n = 1}^{\infty} \frac{1}{n (2 n + 1)}$

Laney Spears 2022-01-22

How to prove monotonicity of this function?
Let $a > 0$ . How to prove that the function:
$f (x) = \frac{a x - 1}{\log (a x)} \cdot \frac{\log x}{x - 1},$
is monotonic (depending on $a < 1$ or $a > 1$ ). I know that we can calculate the derivative and determine its sign, but this needs much of calculation. I'm wondering if we can decide the monotonicity using a simple trick.

Jazmin Perry 2022-01-22

Show that $\int_{1}^{0} \frac{\ln (1 + x)}{x} d x = - \frac{1}{2} \int_{0}^{1} \frac{\ln x}{1 - x} d x$ without actually evaluating both integrals

Jazmin Perry 2022-01-22

Which is bigger among $(i) \log_{23}$ and $\log_{35} (i i) \log_{23}$ and $\log_{311}$ .

tebollahb 2022-01-21

Is there a different approach to evaluate $\int \ln (x) d x$ ?

widdonod1t 2022-01-21

Find $lim_{x \to - \infty} \frac{\ln (1 + 3^{x})}{\ln (1 + 2^{x})}$

zgribestika 2022-01-21

Product of logarithms, prove this identity.

$2 \log (a) \log (b) = \log (a b)^{2} - \log (a)^{2} - \log (b) 2$

for a>1and b>1?

David Young 2022-01-21

Show ${(\log n)}^{(\log n)} = 2^{(\log n) (\log (\log n))}$
I am having difficulty understanding how this follows.
${(\log n)}^{(\log n)} = 2^{(\log n) (\log (\log n))} = n^{\log \log n}$
Which logarithmic identities are used to go through each equality?
e.g. how do you first go from
${(\log n)}^{(\log n)} = 2^{(\log n) (\log (\log n))}$
and then to
$2^{(\log n) (\log (\log n))} = n^{\log \log n}$
(The log base must be 2 or else this equality won't hold)

Gwendolyn Willett 2022-01-21

Why are the domains for ${\ln x}^{2}$ and $2 \ln x$ different?

lugreget9 2022-01-21

A reason for the value of $\int_{0}^{1} \log (x) \log (1 - x) d x$

Lennie Davis 2022-01-21

Prove $\log_{\frac{1}{4}} \frac{8}{7} > \log_{\frac{1}{5}} \frac{5}{4}$

Vikolers6 2022-01-21

Prove $\sum_{{n = 2}}^{\infty} \frac{1}{n \ln (n) \ln \ln n}$ is divergent.

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