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Algebra II

why $\log (n!)$ isn't zero?
I have wondered that why the $\log (n!)$ isn't zero for $n \in N$
Because I think that $\log (1)$ is zero so all following numbers after multiplying the result will become zero.
Thanks in advance.

Ezra Phillips 2022-03-09

Without using logarithms, solve for x in terms of y. Show all steps.
$4^{x - 1} = 16^{2 y}$

Roman Case 2022-03-08

Write each expression as a sum and/or difference of logarithms. Express powers as factors.
1. $\log_{5} (25 x)$
2. $\log_{3} \frac{x}{9}$

chechemua62l 2022-03-08

Write each expression as the sum and/or difference of logarithms.Express powers as factors.
$\log_{5} (\frac{x^{2} + 2 x + 1}{x^{2}}), x > 0$

Thalia Ortiz 2022-03-08

Your friend is asked to simplify the expression $\sqrt{5} + \sqrt{125} - \sqrt{20}$ . He says that since the radicals are unlike, the terms cannot be simplified. Is he correct? If not, explain how he could simplify this expression.

Alisa Duarte 2022-03-07

Working with logarithms
I have an expression involving very small probabilities $A, B, C, D .$
$x \geq \frac{k_{1} B}{A + k_{2} B}$
$x \leq \frac{k_{1} C}{D + k_{2} C}$
Is there any way for me to check if x satisfies the above inequalities using $\log (A), \log (B), \log (C)$ and $\log (D)$ ?

nevinijifg8 2022-03-07

Write each expression as a sum and/or difference of logarithms.Express powers as factors.
$\ln \frac{5 x \sqrt{1 + 3 x}}{{(x - 4)}^{3}}, x > 4$

e3r6a2n1dz60 2022-03-06

Yet another logarithm multiplication doubt
I'm here again, now with a doubt on multiplication on logarithms, I have the expression: $(\log_{5} 2 + \log_{5} 3 \cdot \log_{3} 4) \cdot \log_{2} 5$
I've evaluated it to:
$(\log_{5} 6 \cdot \frac{\log_{5} 4}{\log_{5} 3}) \cdot \frac{1}{\log_{5} 2}$
What should I do with this multiplications ?
EDIT: So, I failed miserably on algebra through, so I evaluated now to:
$= (\log_{5} 2 + \log 5 4) \cdot \log_{2} 5$
$= (\log_{5} 8) \cdot \frac{1}{\log + 52}$
$= \log_{5} (\frac{8}{2})$
$= \log_{5} 4$
So, do I solved it correctly now ? Thank you. EDIT 2:
$= (\log_{5} 2 + \log_{5} 4) \cdot \log_{2} 5$
$= (\log_{5} 8) \cdot \frac{1}{\log_{5} 2}$
$= \frac{\log_{5} 8}{\log_{5} 2}$
$= \log_{2} 8 = 3$

leciazyg 2022-03-03

To calculate: Polynomial equation with real coefficients that has roots 5, $4 - 3 i$ .

Bobrovnik61j 2022-03-03

a) The missing terms for the given polynomial p,q,r, and s such that $q \neq 0 and s \neq 0, \frac{p}{q} \cdot \frac{r}{s} = ?$ .
b) The missing terms given polynomial p,q,r, and s such that $q \neq 0, r \neq 0 and s \neq 0, \frac{p}{q} \div \frac{r}{s} = ?$ .

Layla-Rose Ellison 2022-03-03

Sums and Differences. Evaluate the sum or difference, and write the result in the form $a + b i$ .
$(3 + 2 i) + 5 i and 3 i - (2 - 3 i)$

Tashan Flores 2022-03-03

To calculate: Polynomial equation with real coefficients that has roots 3, $1 - i$ .

hazardetzt10 2022-03-03

If $D = 1 - x^{2} and C = - 1 - 3 x^{2} + 4 x$ , find an expression that equals $3 D - 3 C$ in standard form.

Daanish Wilcox 2022-03-03

How can I find a root of a polynomial, say, $x^{101} + x^{7} - 1$ , without any approximation methods?

tressudasikx 2022-03-03

How do I solve
$x^{4} - x^{3} - 19 x^{2} + 49 x - 30 = 0 ?$

Rosina Mayer 2022-03-03

What is the square root of 300 in radical form?

Ingrid Senior 2022-03-03

What is the limit of the function algebraically, $lim_{x \to - 5} = \frac{x^{2} - 25}{x + 5}$

leciazyg 2022-03-03

What is the magnitude of two complex numbers multiplied together, $Z_{1} \cdot Z_{2}$ ?
$Z 1 = 6.77 + j \cdot 0.09, Z 2 = - 3.27 + j \cdot 6.98$
Three significant digits, fixed point notation.

blakkazn924e4y 2022-03-03

Find the distance between the complex numbers in the complex plane. $1 + 4 i, - 1 + 7 i$

Tajzler6ek 2022-03-02

Find zw and $\frac{z}{w}$ . Write each answer in polar form and in exponential form.
$z = 7 (\cos \frac{π}{4} + i \sin \frac{π}{4})$
$w = 7 (\cos \frac{π}{10} + i \sin \frac{π}{10})$
The product zw in polar form is ? and in exponential form is ?.

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