We Make Solving Algebra 2 Problems and Answers Easy!

High School
Algebra
Algebra II

I need helping with simplifying expression:
$\frac{{(1 + i)}^{33}}{{(1 - i)}^{33}} + {(1 - i)}^{10} + (2 + 3 i) (2 - 3 i) - i^{- 7}$
What I got is:
$\frac{{(1 + i)}^{33}}{{(1 - i)}^{33}} + {(1 - i)}^{10} + (2 + 3 i) (2 - 3 i) - i^{- 7} = \frac{{(1 + i)}^{33}}{{(1 - i)}^{33}} + {(1 - i)}^{10} + 13 - i^{- 7}$
My problems begin with
$\frac{{(1 + i)}^{33}}{{(1 - i)}^{33}}$
is it possible to simplify it without de Moivre or Euler's formulas?

aanvarendbq28 2022-03-30

I am new to logarithms and I am having trouble with this logarithm system.
$\log_{9} (x) + \log_{y} (8) = 2$
$\log_{x} (9) + \log_{8} (y) = \frac{8}{3}$
A step-by-step procedure would be highly appreciated.
Thanks in advance.

Nancy Richmond 2022-03-30

How would I evaluate
$y = e^{2 \frac{\ln 2}{3}} + e^{- \frac{\ln 2}{3}} ?$

peggyleuwpodg 2022-03-30

How to solve exponential function of form $a b^{x} + x = c$ ?
For instance, how would I solve: $3^{x} + x = 85$ ?

ropowiec2gkc 2022-03-30

Proving the limit of $\frac{{\log (n)}^{\log (n)}}{{1.01}^{n}}$
Can anyone please show me a simple way (if there is one) to show that
$lim_{n \to \infty} \frac{{\log (n)}^{\log (n)}}{{1.01}^{n}} = 0$
And that
$lim_{n \to \infty} \frac{{1.01}^{n}}{n!} = 0$
I've checked that it's true, I just need to show it the shortest way possible.

Zack Mora 2022-03-30

Rewrite the rational exponent as a radical by extending the properties of integer exponents.
11 to the two fifths power over 11 to the one fourth power

blestimd4pz 2022-03-30

Rewrite the following exponential expressions as equivalent radical expressions. If the number is rational, write it without radicals or exponents.
$2^{\frac{3}{2}}$

Harold Hoover 2022-03-30

Question about changing a logarithm's base
I've been using the following method to derive/remember the logarithm base conversion formula: If I want to convert $\log_{a} (x)$ to an expression in base b, I say,
$a^{\log_{a} (x)} = x$
$\log_{b} (a^{\log_{a} (x)}) = \log_{b} (x)$
$\log_{a} (x) \log_{b} (a) = \log_{b} (x)$
$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$
It kind of feels like I'm working backwards, and I was wondering if there's a more direct way to go about it. I tried:
$\log_{a} (x) = \log_{a} (b^{\log_{b} (x)})$
$\log_{a} (x) = \log_{b} (x) \log_{a} (b)$
but couldn't rid myself of the loga in the right-hand side of the equation. It occurred to me that if I could rewrite the "a" subscript as " $b^{\log b (a)}$ ", I might be onto something. (Or might not.) Does the notation ever get used like that, where you perform a substitution in a subscript?

Dumaen80p3 2022-03-30

Prove that if $e < y < x$ then $x^{y} < y^{x}$
My try:
I tried to use Taylor's theorem:
$y^{x} - x^{y} = e^{x \ln y} - e^{y \ln x} = 1 + x \ln y + o (x \ln y) - 1 - y \ln x - o (y \ln x) =$
$= {\ln y}^{x} - {\ln x}^{y} + o (x \ln y) - o (y \ln x) = \ln \frac{y^{x}}{x^{y}} + o (x \ln y) - o (y \ln x)$
Hovewer I have a problem to show that $y^{x} - x^{y} > 0$ because I can't say that $\ln \frac{y^{x}}{x^{y}} > 0$ because then I use with theses.
Have you some idea?

metalskaashw 2022-03-29

Prove the inequality $e^{x} \geq x^{e}$ for $x > 0$

There was a sample of
300
milligrams of a radioactive substance to start a study. Since then, the sample has decayed by
2.3%
each year.

Let
t
be the number of years since the start of the study. Let
y
be the mass of the sample in milligrams.

Write an exponential function showing the relationship between
y
and
t
.

Sage Fry 2022-03-28

Consider the exponential equation. $9^{x} = 733$
a. Find x in exact form: $x = b$ . Approximate x, correct to at least 3 decimal places: $x =$
b. Approximate $x$ , correct to at least 3 decimal places: $x =$

Janiyah Hays 2022-03-28

$10^{- 9} [2 \times 10^{6} + 3^{1000}]$
I'm stuck on solving this. I wasn't able to put this into my calculator since the number is too big for it to calculate.
So far I've done this:
$2 \times 10^{- 3} + 3^{1000} \times 10^{- 9}$
log the equation
$\log [2 \times 10^{- 3} + 3^{1000} \times 10^{- 9}]$
$\log (2 \times 10^{- 3}) + \log (3^{1000} \times 10^{- 9})$
$(\log 2 + {\log 10}^{- 3}) + ({\log 3}^{1000} + {\log 10}^{- 9})$
$(\log 2 - 3) + (1000 \times \log 3 - 9)$
How do I get rid of the log afterwards?

monkeyman130yb 2022-03-28

$\ln r + \ln q = k r$ Isolating $r$

rhedynogh0rp 2022-03-28

$\int \frac{f}{f^{'}} d x = \int \frac{1}{{(\ln f)}^{'}} d x = ?$
I recently saw in another post that ${(\ln f)}^{'} = \frac{f^{'}}{f}$
where $f = f (x)$
From which it follows that $\int \frac{f^{'}}{f} d x = \int {(\ln f)}^{'} d x = \ln f + C$
What about integrating the inverse of this?
I.e. what about $\int \frac{f}{f^{'}} d x = \int \frac{1}{{(\ln f)}^{'}} d x = ?$

Jaylin Clements 2022-03-28

Proving that $\sum_{{n = 1}}^{\infty} \frac{{(- 1)}^{n + 1}}{n} = \log 2$

metalskaashw 2022-03-27

difference of logs
$\log (a - b) - \log (a - c)$
oes this have a simpler form? Perhaps one where the as have cancelled out? I know it can also be expressed as a log of the fraction: $\log \frac{(a - b)}{(a - c)}$ , but the same question applies.

Guadalupe Glass 2022-03-27

Continuing logarithm $\log (\log (\dots \log (z)))$

Paula Good 2022-03-27

Consider a function $f : C \mapsto R$ . As far as I know, for this function $f (x, y) = u (x, y) + i v (x, y)$ to be analytic, it must satisfy the Cauchy-Riemann conditions, which state:
$\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}$
$\frac{\partial u}{\partial y} = - \frac{\partial v}{\partial x}$
Of course, v(x,y)=0. This implies that u(x,y)=C where C is constant, and thus the only real function of a complex variable is f(z)=C.
This cannot be right, surely?

ezpimpin6988ok1n 2022-03-27

How can you figure out this algebraic math problem? The physics class has built a ramp. The ramp is 60 centimeters tall at the highest point and has a horizontal length of 100 centimeters. What is the length of the ramp, in simplified radical form?

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.

Algebra II

Expert Answers to Algebra 2 Problems