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Recent questions in Logarithmic Functions

iamerkviladzekiu 2023-02-09

value of $= l o g_{625} \sqrt 5$

inhaltynuaddyh4b 2023-02-08

What is the derivative of $y = \log_{3} (x)$ ?

Scarlet Mcpherson 2023-02-05

What is the derivative of $e^{5}$ ?

Elaina Mullen 2023-01-29

How to differentiate $y = \ln (x^{3})$ ?

Seamus Livingston 2023-01-27

How to find the derivative of ${\ln x}^{4}$ ?

Nash Cox 2022-12-14

What is $\log 5$ ? How can we find logs of numbers without using a calculator?

gheadarce 2022-11-24

Find the derivative of the function
$y = \ln (\frac{x}{x + 5})$
$y^{'} = ?$

BertonCO5 2022-11-23

If $x^{x} y^{y} z^{z} = c$ , show that at $x = y = z, z_{x y} = - (x \log x)^{- 1}$
I applied logarithmic functions on both sides, ultimately it led to a satisfying result where most things canceled out, but unfortunately, it wasn't the right answer.

Ernesto Wagner 2022-11-23

How to solve an equation like $2^{x} + x = 2$ ?

armlanna1sK 2022-11-23

If $f (n) = (\sqrt{n})^{\sqrt{n}}$ and $g (n) = (\lg n)^{n}$ , is $f (n) = O (g (n))$ or $g (n) = O (f (n))$ ?

Emma Hobbs 2022-11-22

Let $L (X) = \exp (\sqrt{\log X \log \log X})$
Prove that if c>0, $Y = L (X)^{c}$ , and $u = \log X / \log Y$ , then
$u^{u} = L (X)^{(1 / 2 c) (1 + o (1))}$
I've tried to write $u^{u} = (\log X / \log Y)^{\log X / \log Y}$
But that doesn't seem to get me anywhere.

Abdiel Mays 2022-11-21

If the function $f (x) = \log_{2 x} x^{2}$ is given, what is $f^{'} (4)$ ?
I tried to use the formula for derivative of logarithm but here the base is 2x, so it made me confused.
Note that the answer is $1 / (18 \ln 2)$

Clara Dennis 2022-11-20

The function is
$\int \frac{1}{1 + \sqrt{2 x}} d x$
Using $u = 1 + \sqrt{2 x}$ , $d u = \frac{1}{\sqrt{2 x}} d x$ . Which gives us
$\sqrt{2 x} \int \frac{1}{u} d u$
The final answer of this would give $\sqrt{2 x} \ln | 1 + \sqrt{2 x} |$ , but when I checked my answer the correct answer is $\sqrt{2 x} - \ln | 1 + \sqrt{2 x} |$

Audrey Arnold 2022-11-19

Let $f (x, y) = \sqrt[4]{x y^{3}}$ . Find the percent change $\frac{d f}{f}$ in the function f if the percent change in x is 4% and the percent change in y is 3%

Rigoberto Drake 2022-11-19

Solve each of the following equations for x.
a) $\ln (5 x) = 0 x = ?$
b) $\log_{5} (2 x) + \log_{5} (4 x) = 2 x = ?$

ajumbaretu 2022-11-18

Expressing $\frac{2 x^{2} - 9 x - 6}{x (x^{2} - x - 6)}$ in partial fraction would give you: $\frac{16}{5 (x + 2)}$
Given that $\int_{4}^{6} \frac{2 x^{2} - 9 x - 6}{x (x^{2} - x - 6)} d x = l n \frac{m}{n},$ determine the values for the integers m and n.

Kareem Mejia 2022-11-18

Find the derivative of the logarithmic functions:
$y = \ln (12 x - 4)$

Fahdvfm 2022-11-18

Evaluate each expression
$a) \log_{5} \frac{1}{25} = ?$
$b) \log_{2} 32 = ?$

Siemensueqw 2022-11-17

We can combine $2 \log x + \log y - \log z$ to get ???

Kameron Wang 2022-11-17

If the function $f (x) = \frac{l n (x)}{x}$ where x>0, has a maximum at ( $(e, \frac{1}{e})$ ) compare the numbers $e^{π}$ and $π^{e}$
$l n (x)$ is the natural logarithmic function i.e the logarithmic function with base e.

Logarithmic functions are a type of mathematical tool used to express large numbers in a more manageable form. They simplify complex calculations by converting exponential equations into linear ones, and are commonly used in fields such as engineering, science, and economics. These functions can be used to identify trends in data sets, measure changes in magnitude, and compare different sets of data. They are also useful for solving equations with exponential or power functions. To master logarithmic functions, it is helpful to practice solving problems and equations. These skills are important for quickly and accurately solving complex math problems and can be applied in various areas of life.

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