We Make Solving Algebra 2 Problems and Answers Easy!

High School
Algebra
Algebra II

How to show that $- \log_{b} x = \log_{\frac{1}{b}} x$

Jasiah Vincent 2022-04-08

How to prove this ln inequality?
I have the following inequality, which (supposedly) holds for every $x \in R$
$1 + x \ln (x + \sqrt{1 + x^{2}}) \geq \sqrt{1 + x^{2}}$
I've been struggling to find some known inequalities involving logarithms that could be applied here (and lack of condition for x to be non-negative doesn't help either). I would be very helpful for hints on how this should be approached.

Freddy Novak 2022-04-08

How to prove derivative of logarithm with base $b$ ?
I learned how to derive a logarithm with any base. This is the formula:
$\frac{d}{d x} \log_{b} x = \frac{1}{x \ln b}$
How can it be proved?

Blaine Jimenez 2022-04-08

Using complex variables to evaluate real trig integral
$\int_{0}^{2 π} \frac{\cos (2 θ)}{1 - 2 a \cos (θ) + a^{2}} d θ, - 1 < a < 1$
I did the substitution $z = e^{i θ}$ and then got $\cos (2 θ) = \frac{1}{2} (z^{2} + \frac{1}{z^{2}})$ ,so
$\int_{0}^{2 π} \frac{\cos (2 θ)}{1 - 2 a \cos (θ) + a^{2}} d θ = \frac{1}{i} \int_{| z | = 1} \frac{\frac{1}{2} (z^{2} + \frac{1}{z^{2}})}{1 - a z - \frac{a}{z} + a^{2}} d z .$
Did I make a mistake here?

Breanna Fisher 2022-04-08

Use properties of logarithms to condense the logarithmic expression . Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator.
$3 \ln x - \frac{1}{3} \ln y$

Alan Zavala 2022-04-07

Finding the coefficient of $x^{n}$ in the expansion of ${{({\log_{e} (1 + x)})}^{2}}$
I've been trying to find the coefficient of xn in the expansion of ${({\log_{e} (1 + x)})}^{2}$ .I wrote out the expansion of ${{({\log_{e} (1 + x)})}^{2}}$ explicitly and tried to generalize the terms involving $x^{n}$ , but...so far no luck.
Is there any other alternative ?

Santos Mooney 2022-04-07

Find the solution for the exponential equation in terms of logarithms. $\frac{8 x}{2} = 5^{1 - x}$

Max Williams 2022-04-07

Find the sum and product of the complex numbers $1 - 4 i$ and $- 1 + 6 i$

Karla Thompson 2022-04-07

Find the product of the complex numbers
$z_{1} = 4 ({\cos 50}^{\circ} + i {\sin 50}^{\circ})$
and $z_{2} = 7 ({\cos 100}^{\circ} + i {\sin 100}^{\circ})$
Leave the answer in polar form.

Angelina Kaufman 2022-04-07

I'm quite ashamed that I'm at a math-related course at the university and I'm stuck. I can't solve at all this equation:
$n = 8 \log_{2} (n) .$
I have tried applying the log property so it becomes $2^{n} = 2^{8 n}$
Besides that this didn't help me, I'm not even sure if I applied right the property that says $x = \log_{2} (y) \Rightarrow 2^{x} = y$
Thanks in advance! Best Regards,

Izabelle Walsh 2022-04-07

I want to find this limit for complex variable z
$lim_{z \to - 1} (z + 1) \sin (\frac{1}{z + 1})$
In the real case I know sin(z) is bounded by -1,1, and the limit is 0. But in the complex case $\sin (z)$ is not bounded. How can I find the limit or prove that it doesn't exist?

Alan Zavala 2022-04-07

I need to find all complex number z such that $z^{2} + (- 7 - 7 i) z + 49 i = 0$ while using the quadratic formula. I’ve got $z = \frac{(7 + 7 i) \pm \sqrt{- 147 i}}{2}$ and then I don’t know what to do next. Can anyone help?

Gustavo Lam 2022-04-07

How to prove that $\cos^{2} (z) + \sin^{2} (z) = 1$ , where z is a complex variable (if it is true)?

Njd gang2022-04-06

Blaze Shepherd 2022-04-06

For every real number $a > 0$ . Find all complex number z, satisfying the equation $z | z | + a z + i = 0$

Gretchen Barker 2022-04-06

Find the quotient $\frac{z_{1}}{z_{2}}$ of the complex numbers $z_{1} = 20 ({\cos 75}^{\circ} + i {\sin 75}^{\circ})$
$z_{2} = 4 ({\cos 25}^{\circ} + i {\sin 25}^{\circ})$
Leave answers in polar form.

Willie Kelley 2022-04-06

Find the product $z_{1} z_{2}$ and the quotient $\frac{z_{1}}{z_{2}}$ . Express your answers in polar form.
$z_{1} = \frac{7}{8} (\cos (35^{\circ}) + i \sin (35^{\circ})), z_{2} = \frac{1}{8} (\cos (135^{\circ}) + i \sin (135^{\circ}))$
$z_{1} z_{2} = ?$
$\frac{z_{1}}{z_{2}} = ?$

Kali Thomas 2022-04-06

Find the product of the complex numbers.Leave answers in polar form.
$z_{1} = 4 (\cos \frac{3 π}{7} + i \sin \frac{3 π}{7})$
$z_{2} = 10 (\cos \frac{4 π}{7} + i \sin \frac{4 π}{7})$

Merati4tmjn 2022-04-06

Evaluate $8 \times 9 - 7 + 6 \times (15 - 15)$ .

Elle Weber 2022-04-06

Compute $9 \div 9 - 14 \times (9 + 11) \times 11$ using the correct order of operations.

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