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Algebra II

Find all solutions of x 2 − x + 2 = 0 over Z5.

broggesy9 2022-04-28

Product rule for logarithms works on any non-zero value?
The product rule for logarithms states that:
$\log_{b} M + \log_{b} N = \log_{b} (M \cdot N)$
Most sources that I've found* state that this rule only applies when M and N are positive. It's true that $\log_{b} 0$ is undefined, but negative values in place of M and N seem to work just fine:
$\log (- 1) + \log (4) = \log (- 1 \cdot 4)$
Why the discrepancy?

Kaiya Hardin 2022-04-28

Is it standard to say $- i \log (- 1)$ is $π$ ?

veleumnihryz 2022-04-28

Simplify expression using the properties of logarithms.
$3 \log_{4} r^{2} - 2 \log_{4} r$

livinglife100s8x 2022-04-27

If $x = \log_{12} 27$ ,then what is the the value of $\log_{616}$ ?

diasenamorn5l 2022-04-27

Way to calculate exponent in congruent equation
I want to solve
$5^{x} \equiv 21 (mod 23)$
Is there a way to get the $x$ without trial & error?

Maurice Maldonado 2022-04-27

Solution for $\log_{7} x + \log_{\frac{1}{7}} x^{2} = \log_{49} x - 3$

Assume that 2 cards are drawn from a standard 52-card deck. Find the following probabilities

a) Assume the cards two non-black cards are drawn without replacement. Find the probability
of drawing a
non-black card
followed by
a non-black card

b) Assume the two non-black cards are drawn with replacement. Find the probability
of drawing a
non-black card
followed by
a non-black card.

Jaidyn Cook 2022-04-26

How to determine $lim_{n \to \infty} n \ln (1 + \frac{1}{n})$

tefoldaavv 2022-04-26

How $a^{\log_{b} x} = x^{\log_{b} a}$

Deven Livingston 2022-04-26

What is intresting about
$\sqrt{\log_{x} \exp \sqrt{\log_{x} \exp \sqrt{\log_{x} \exp \dots}}} = \log_{x} e$
Why does
$\sqrt{\log_{x} \exp \sqrt{\log_{x} \exp \sqrt{\log_{x} \exp \dots}}} = \log_{x} e = \frac{1}{\ln x}$
There only seems to be a relation when using square roots, but not for cubed roots or anything else. Why does this equation work and why does it only work for square roots?
(The $e$ is not significant, by the way. You could give the exponential function a different base, $a$ , and say the equation equals $\log_{x} a)$ .

Bronson Olson 2022-04-26

What is solution of this equation
I am new to logarithms, I am confused what to do when any constant is raised to a power such as $1 + \log x$ .
As in this equation, $9^{1 + \log x} - 3^{1 + \log x} - 210 = 0$
While I try to take log on both sides, things get messy.
All the logs have base 3.

dolovatgyp 2022-04-26

Simplify expression using the properties of logarithms
$\log_{53} k + \log_{57} k^{3}$

caldaridvq 2022-04-26

simplify natural logarithm
How to simplify this natural logarithm
$\frac{1}{2} \ln | y + 1 | - \frac{1}{2} \ln | y - 1 | + \ln | C | = \frac{1}{2} \ln | x + 1 | - \frac{1}{2} \ln | x - 1 |$
if I apply the logarithm rule
$\ln \sqrt{| y + 1 |} - \ln \sqrt{| y - 1 |} + \frac{1}{2} \ln (C^{2}) = \ln \sqrt{| x + 1 |} - \ln \sqrt{| x - 1 |}$
Please help further..

Daniel Joler2022-04-26

The combined area of a square and a rectangle is 225 square yards. the length of the rectangle is 8 times the width of the rectangle and the length of a side of the square is the same as the width of the rectangle. find the dimensions of the square and the rectangle.

Daniel Joler2022-04-26

The product of two numbers is 26 and one of the numbers is one larger than six times the other number. find the numbers.

Daniel Joler2022-04-26

suppose that the combined area of two squares is 104 square inches. Each side of the larger square is five times as long as a side of the smaller square. find the size of each square.

pacificak8m 2022-04-25

Is Lim X infinity $(\sqrt{x} - \sqrt{x - 3}$ ?

redupticslaz 2022-04-25

How can I show that $lim_{x \to \infty} \frac{\log (x + 1)}{\log x} = 1 ?$

Gage Potter 2022-04-25

Using laws of logarithms, write the expression in the image as a single logarithm.
$6 \log (64 - x^{2}) - (\log (8 + x) + \log (8 - x) = \log ()$

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