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Recent questions in Logarithmic Functions

Hanna Webster 2022-11-14

a) Rewrite as an exponential equation.
$\ln 5 = y$
b) Rewrite as a logarithmic equation
$e^{7} = x$

Ayanna Goodman 2022-11-14

If the expansion of the logarithmic integral is
$li (n) = \log \log n + γ + \sum_{k = 1}^{\infty} \frac{(\log n)^{k}}{k! k}$
what is the inverse of the function?

Juan Lowe 2022-11-14

Solve for y in the equation below
$4^{- 6 y} = 11$

vedentst9i 2022-11-13

Find the x-intercept of:
$3 - 4 \log_{10} (2 x)$
My process:
$4 \log_{10} (2 x) = 3$
$\log_{10} (2 x) = \frac{3}{4}$
How would I find the x-intercept from here?
$\log_{10} (2 x) = \log_{10} (?)$
2x=?
xintercept=(?)/(2)
How do I find the x-intercept?

Ty Moore 2022-11-12

What are the differences between linear quadratic exponential and logarithmic functions?

Adison Rogers 2022-11-12

The function is
$G (x) = 4^{\frac{C}{x}}$
I have $u = \frac{C}{x}$ , then I calculate
$\frac{d}{d u} 4^{u} = u (4)^{u - 1}$
But does
$\frac{d}{d x} \frac{C}{x} = C$
because I don't know if C is a constant or a independent variable.

inurbandojoa 2022-11-12

Why does $f (x y) = f (x) + f (y) ⟹ f (x) = k \ln x$
My textbook says $f (x y) = f (x) + f (y) ⟹ f (x) = k \ln x$
But if I'm not mistaken, f(x) could be a logarithmic function with any base? So why only $\ln x$ ?

Karley Castillo 2022-11-11

Express the equation in exponential form.
a) $\log_{3} (27) = 3$
b) $\log_{3} (1) = 0$

charmbraqdy 2022-11-11

If $\ln a = 2, \ln b = 3, and \ln c = 5$ , evaluate the following:
a) $\ln (\frac{a^{4}}{b^{3} c^{4}}) = ?$
b) $\ln \sqrt{a^{4} b^{1} c^{1}} = ?$

pighead73283r 2022-11-11

Exponential and Logarithmic Functions
Find: $\log_{2} (x^{2} - 4 x - 28) = 2$

Audrey Arnold 2022-11-11

Find Difficult Indefinite Integral $\int (\log x + 1) x^{x} d x$

tramolatzqvg 2022-11-10

How to solve these given?
$y = e^{\sqrt{x^{2} - 16}}$

Siemensueqw 2022-11-09

Prove that $\frac{d}{d x} (\ln | x |) = \frac{1}{x}, x \neq 0$

Adrian Brown 2022-11-08

Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.
$\log (z y^{3}) = ?$

Jenny Roberson 2022-11-07

Is there a closed-form solution for the integral
$\int_{0}^{\infty} \log_{2} (1 + a x) \cdot e^{- b x} d x$
with $a, b \geq 0$ ?

Aryanna Fisher 2022-11-05

Given the equation $p = \frac{2 x}{y}$ , find $\frac{d y}{d t}$

Yaretzi Mcconnell 2022-11-05

$f (x) = 2^{x}$
$g (x) = x^{2} + 3 x - 3$
For what positive integer values of x is f(x)>g(x)?
A) x<6 and x>1
B) x<2 and x>5
C) x<5 and x>2
D) x<1 and x>6

Jonas Huff 2022-11-05

Solve for x
$\log_{4} (x - 3) = 1 - \log_{4} (x - 6)$

Madison Costa 2022-11-04

Find x in the following logarithmic functions:
$a) \log_{10} x = 2 b) \log_{10} x = - 3 c) \log_{10} x = \frac{1}{2}$

Mark Rosales 2022-11-04

Solve each logarithmic equation.Express irrational solutions in exact form and as a decimal rounded to three decimal places.
$\log (2 x + 1) = 1 + \log (x - 2)$

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.

Calculus 1

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