Build Your Logarithms Skills with Engaging Lessons and Exercises

How do you simplify a log with an exponent in the base?
Suppose you had:
$\log_{x^{b}} (y)$
How can you simplify this? Do you use the change of base formula?
Note: I tried to come up with something similar to a homework problem without actually being a homework problem. I think this is the most simple form.

gea3stwg 2022-01-21

Joint Entropy closed-form analytical solution
Differential entropy of a single Gaussian random variable is
$H (X) = \frac{1}{2} \ln (2 π e σ 2)$
What then is the closed-form analytical solution for joint entropy, H(X,Y)?

David Rojas 2022-01-21

Log integrals I
In this example the value of the integral
$I_{3} = \int_{0}^{1} \frac{\ln^{3} (1 + x)}{x} d x$
was derived. The purpose of this question is to determine the value of the more general form of the integral, namely,
$I_{n} = \int_{0}^{1} \frac{\ln^{n} (1 + x)}{x} d x .$
Also is there a corresponding value for the integral
$J_{n} = \int_{0}^{1} \frac{\ln n (1 + x)}{1 + x} d x ?$

siutulysr5 2022-01-21

Prove by Mean Value Theorem $\frac{x}{1 + x} < \ln (1 + x) < x for x > 0$

PEEWSRIGWETRYqx 2022-01-21

How can I prove that $x - \frac{x^{2}}{2} < \ln (1 + x)$

Kristina Mcclain 2022-01-20

How did my professor change this logarithm into the next one?
Logarithms are a weak point for me and Im

kuntungw3 2022-01-20

Expand the expression into a sum, difference, and/or multiple of logarithms:
${\log (\frac{a^{2} b}{c})}^{3}$

Autohelmvt 2022-01-20

Express as sums or differences of logarithms.
$\log (\frac{x^{3}}{y z^{5}})$

Vilharjevw7 2022-01-20

$\log_{7} n$ is either an integer or an irrational number

Krzychau1 2022-01-20

Closed form for the partial sum $\sum_{k = 1}^{n} \frac{\ln k}{k}$

interdicoxd 2022-01-20

Write the logarithmic expression
$\log (\sqrt[3]{\frac{x^{- 12} y^{7}}{z^{- 14}}})$
as an expression involving three separate logarithms

Wanda Kane 2022-01-20

How do I find the common logarithm of a number?

Annette Sabin 2022-01-20

Evaluate the log expression
$\frac{1}{\log_{x y} (x y z)} + \frac{1}{\log_{y z} (x y z)} + \frac{1}{\log_{z x} (x y z)}$

William Boggs 2022-01-20

Prove that $\frac{x}{x + 1} < \ln (1 + x) < x$ for $x > - 1, x \neq 0$

burkinaval1b 2022-01-20

Why does logarithmic differentiation work even if logs are not defined for negative numbers?

Gregory Jones 2022-01-20

How to solve for negative numbers in logarithmic equations
I am trying to solve the equation
$z^{n} = 1 .$
Taking $\log$ on both sides I get $n \log (z) = \log (1) = 0$ .
$\Rightarrow n = 0$ or $z = 1$ .
But I clearly missed out $(- 1)^{even numbers}$ which is equal to $1$ .
How do I solve this equation algebraically?

pogonofor9z 2022-01-20

Is showing $lim_{z \to \infty} {(1 + \frac{1}{z})}^{z}$ exists the same as $lim_{n \to \infty} (1 + \frac{1}{n})$ n exists

Adela Brown 2022-01-20

Iterative calculation of $\log x$
Suppose one is given an initial approximation of $\log x, y_{0},$ so that:
$y_{0} = \log x + ϵ \approx \log x$
Here, all that is known about x is that $x > 1$ . Is there a general method of improving that estimation using only addition & multiplication, i.e. without exponentiation or logarithms?
$y_{1} = f (y_{0}, x) = ?$

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