Express radical

smileycellist2
2021-07-17
Answered

Express radical

You can still ask an expert for help

Alannej

Answered 2021-07-18
Author has **104** answers

The answer given in the photo below

Answered 2021-12-24

Given:

Solution:

Answer: simplest form of the radical expression

asked 2022-04-03

Solving $x}^{\mathrm{log}\left(x\right)}=\frac{{x}^{3}}{100$

How do I find the solution to:

$x}^{\mathrm{log}\left(x\right)}=\frac{{x}^{3}}{100$

So I multiplied 100 both sides getting:

$100{x}^{\mathrm{log}\left(x\right)}={x}^{3}$

Now what should I do?

How do I find the solution to:

So I multiplied 100 both sides getting:

Now what should I do?

asked 2022-05-03

Rewrite the following exponential expressions as equivalent radical expressions. If the number is rational, write itwithout radicals or exponents.

$4}^{-\frac{3}{2}$

asked 2021-02-02

Сalculate whetger the vectors u and v are parallel, orthogonal or neither.

$u=\u27e85,3\u27e9,u=\u27e8\frac{10}{4},-\frac{3}{2}\u27e9$

asked 2022-06-24

How to prove if log is rational/irrational

I'm an English major, now doubling in computer science. The first course I'm taking is Discrete Mathematics for Computer Science, using the MIT 6.042 textbook.

Within the first chapter of the book's practice problems, they ask us multiple times to prove that some log function is either rational or irrational.

Specific cases make more sense than others, but I would really appreciate any advice on how to approach these problems. Not how to carry them out algebraically, but what thought constructs are necessary to consider a log being (ir)rational.

For example, in the case of ${\sqrt{2}}^{2{\mathrm{log}}_{2}3}$, proving that $2{\mathrm{log}}_{2}3$ is irrational (and therefore ${a}^{b}$, when $a=\sqrt{2}$ and $b=2{\mathrm{log}}_{2}3$ is rational) is not an easily solvable problem. I understand the methods of proofs, but the rules of logs are not intuitive to me.

A section from my TF's solution is not something I would know myself to construct:

Since $2<3$ we know that ${\mathrm{log}}_{2}3$ is positive (specifically it is greater than 1), and hence so is $2{\mathrm{log}}_{2}3$. Therefore, we can assume that a and b are two positive integers. Now $2{\mathrm{log}}_{2}3=a/b$ implies ${2}^{2{\mathrm{log}}_{2}3}={2}^{a/b}$. Thus

${2}^{a/b}={2}^{2{\mathrm{log}}_{2}3}={2}^{{\mathrm{log}}_{2}{3}^{2}}={3}^{2}=9\text{,}$

and hence ${2}^{a}={9}^{b}$

Any advice on approaching thought construct to logs would be greatly appreciated!

I'm an English major, now doubling in computer science. The first course I'm taking is Discrete Mathematics for Computer Science, using the MIT 6.042 textbook.

Within the first chapter of the book's practice problems, they ask us multiple times to prove that some log function is either rational or irrational.

Specific cases make more sense than others, but I would really appreciate any advice on how to approach these problems. Not how to carry them out algebraically, but what thought constructs are necessary to consider a log being (ir)rational.

For example, in the case of ${\sqrt{2}}^{2{\mathrm{log}}_{2}3}$, proving that $2{\mathrm{log}}_{2}3$ is irrational (and therefore ${a}^{b}$, when $a=\sqrt{2}$ and $b=2{\mathrm{log}}_{2}3$ is rational) is not an easily solvable problem. I understand the methods of proofs, but the rules of logs are not intuitive to me.

A section from my TF's solution is not something I would know myself to construct:

Since $2<3$ we know that ${\mathrm{log}}_{2}3$ is positive (specifically it is greater than 1), and hence so is $2{\mathrm{log}}_{2}3$. Therefore, we can assume that a and b are two positive integers. Now $2{\mathrm{log}}_{2}3=a/b$ implies ${2}^{2{\mathrm{log}}_{2}3}={2}^{a/b}$. Thus

${2}^{a/b}={2}^{2{\mathrm{log}}_{2}3}={2}^{{\mathrm{log}}_{2}{3}^{2}}={3}^{2}=9\text{,}$

and hence ${2}^{a}={9}^{b}$

Any advice on approaching thought construct to logs would be greatly appreciated!

asked 2022-02-04

How do you multiply $6a({a}^{2}+2ab+{b}^{2})$ ?

asked 2022-03-30

asked 2021-10-10

Based on the definition of logarithms, what is ${\mathrm{log}}_{10}1000$