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Algebra II

Evaluate the expression without using a calculator.
$e^{2 \ln 7}$

Averie Ferguson 2022-04-03

Does the logistic function uniquely satisfy these three conditions?
Given
$r (t) = \frac{f (t)}{1 - F (t)}$ {Eq. 1}
where
$f (t) = \frac{d F}{d t}$ {Eq. 2}
and the conditions:
$lim_{t \to \infty} r (t) = 1$ {Eq. 3}
$lim_{t \to \infty} F (t) = 1$ {Eq. 4}
$lim_{t \to \infty} f (t) = 1 - F (t)$ {Eq. 5}
I can think of just one function F satisfying these three conditions--the logistic function:
$F (t) = \frac{1}{1 + e^{- t}}$ {Eq. 6}
(which can also be expressed $F (t) = r (t)$ )
Is this is the only function satisfying these conditions? If so, is there a way to prove it?

Oxinailelpels3t14 2022-04-03

The expression with rational exponents as a radical expression.
$5 \times x$ to the one fourth power

blestimd4pz 2022-04-03

Stuck on a log equation
I am having trouble figuring out how I can solve this log:
$6 \log (x^{2} + 1) - x = 0$
The steps i've thought to take so far are as follows:
step 1: subtract the right most x to the other side of the equation:
$6 \log (x^{2} + 1) = x$
step 2: divide by 6:
$\log (x^{2} + 1) = \frac{x}{6}$
step 3: make both sides an exponent of 10 to get rid of the log:
$x^{2} + 1 = 10^{\frac{x}{6}}$
step 4. ??????????????

sexoagotadorogyr 2022-04-03

State domain, range, vertical asymptote and $x, y$ intercepts for $\log_{4} (x - 1) + 1$

Rex Maxwell 2022-04-03

Solving $x^{\log (x)} = \frac{x^{3}}{100}$
How do I find the solution to:
$x^{\log (x)} = \frac{x^{3}}{100}$
So I multiplied 100 both sides getting:
$100 x^{\log (x)} = x^{3}$
Now what should I do?

markush35q 2022-04-03

Solving an exponential equation
Alright, here's the equation:
$‎ {1.08}^{x} = {1.10}^{x - 1}$
I know I need to use logarithms, but I can't figure how to do it. Thanks in advance!

Aleah Choi 2022-04-03

Solving equation $\log_{y} (\log_{y} (x)) = \log_{n} (x)$ for n
I'm just wondering, if I log a constant twice with the same base y,
$\log_{y} (\log_{y} (x)) = \log_{n} (x)$
Can it be equivalent to logging the same constant with base n? If yes, what is variable n equivalent to?

siliciooy0j 2022-04-02

Find all real solutions to the equation $3^{1 + 2 \log_{3} (y - x)} = 48$
With this problem I have difficulty getting rid of the exponent.
$2 \log_{5} (2 y - x - 12) = \log_{5} (y - x) + \log_{5} (y + x)$

Guadalupe Glass 2022-04-02

Exponential and logarithmic series: Find the sum of
$2^{2} + \frac{3^{2}}{2}! + \frac{4^{2}}{3}! + \dots$ to infinity

palmantkf4u 2022-04-02

Evaluate expression using change of base
This is an awkward question to me, it was not covered in class.
Suppose:
$\log_{b} 2 = A$
$\log_{b} 3 = B,$
$\log_{b} 5 = C$
Then, use the change-of-base formula to evaluate
$\log_{b^{2}} 5$
and
$\log_{\sqrt{b}} 2 .$
As an example answer, we're given $\log_{3} b$ becomes $\frac{1}{B}$
Hopefully someone understands where they're coming from.

ideklaraz7xz 2022-04-02

Equation with Logarithm
I want to solve the following equation:
$3^{x} 3^{x - 1} = 243 .$
My approach is the following:
$3^{2 x - 1} = 243$ then
$(2 x - 1) \cdot \log 3 = \log 243$ and then:
$x = \frac{\frac{\log 243}{\log 3} + 1}{2}$
Is this correct?

Petrolovujhm 2022-04-02

The distance from the origin to the point that corresponds to a complex number is known as the modulus of that complex number. There is an interesting relationship involving the moduli of two complex numbers and the modulus of their product. Spread the work around everyone try a few examples and try to figure out what this relationship is.

jermandcryspza3 2022-04-02

Suppose that $G (x) = \log_{3} (2 x + 1) - 2 .$
(a) What is the domain of $G$ ?
(b) What is $G (40)$ ? What point is on the graph of $G$ ?
(c) If $G (x) = 3$ , what is x? What point is on the graph of $G$ ?
(d) What is the zero of $G$ ?

rhedynogh0rp 2022-04-02

Steps to calculate $\log_{2} 0.667$
This could be a basic question. But I would like to know steps I should follow to calculate $\log_{2} 0.667$

Lucian Ayers 2022-04-02

Solving $8 n^{2} = 64 n \log (n)$

Pasegeabe85xy 2022-04-02

Rewrite the rational exponent as a radical.
$(5 \cdot \frac{3}{4} power) \frac{2}{3}$ power

Oxinailelpels3t14 2022-04-02

Rewrite the radical expression as an expression with rational exponents. fifth root of x to the power of 9

The majority of Algebra 2 homework will be almost the same for college students these days since the only changes will relate to a practical application like business solutions, financial challenges, and certain problems where formulas and concepts are applicable. Looking for Algebra 2 answers, you will find some solutions below that are most likely to answer your Algebra 2 problems and answers. If you’re a high-school learner, there are Algebra 2 questions for you as well with provided solutions. The most important is to share your instructions and read through examples that address various Algebra 2 questions and answers.

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