Tagged Questions
6
votes
6answers
358 views
How is this proof flawed?
$\sqrt{x}=-1$
$\sqrt{x}^2=(-1)^2$
$x=1$
Now substitute it into the original equation
$\sqrt{1}=-1$
$1=-1$
4
votes
4answers
67 views
Can you raise a Matrix to a non integer number? [duplicate]
So I heard you can take a matrix A to the power 2, take it to a -3th power and multiply it by an irrational number. You can also do some other non-intuitive things like taking e to the power of a ...
1
vote
1answer
68 views
Units in exponent - e.g. solve: $2^{3 years}$
What happens to units in an exponent?
My math textbook just introduced the exponential equation:
$$A_t = Pe^{rt}$$
I've always made it a point in solving math problems to include the units in every ...
6
votes
3answers
148 views
What's the intuition behind non-integer exponents/powers
Consider some $a \in \mathbb{R}$ and $x \in \mathbb{R}\backslash \mathbb{N}$.
Is there some intuition to be had for the number $a^x$?
For example the intuition of $a^2$ is obvious; it's $a*a$ which ...
3
votes
3answers
95 views
What is the difference between exponentials and powers?
I am a java programmer. But I have a doubt regarding a mathematics. There was a method called Math.exp(double a) description:Returns Euler's number e raised to the power of a double value. and another ...
0
votes
2answers
66 views
Exponentation vs Power
What definition of $a^b$ operation is the most popular and standartized: Exponentation or Power?
Is any difference between them?
0
votes
3answers
114 views
Get the number, knowing the power and result of raising.
If I have a number and a power of this number. How to get the number that raised to the known power will give the known number?
$$x^3 = 90$$
How to get $x$?
1
vote
2answers
374 views
Find all solutions to the equation $e^z = i$
I know that there is an equation for finding the nth roots of a complex number, which easily done once you have the modulus and argument of the complex number in question. There would be n roots. But ...
49
votes
4answers
971 views
Complexity class of comparison of power towers
Consider the following decision problem: given two lists of positive integers $a_1, a_2, \dots, a_n$ and $b_1, b_2, \dots, b_m$ the task is to decide if $a_1^{a_2^{\cdot^{\cdot^{\cdot^{a_n}}}}} < ...
2
votes
2answers
164 views
Solving $x^\frac{1}{x}=y$ for $x$
I've tried everything: Taking $\ln$ of both sides, raising to the power $x$, nothing seems to work.
Is there a way to solve this or am I going to have to use numerical methods instead?
6
votes
3answers
475 views
What we can say about $-\sqrt{2}^{-\sqrt{2}^{-\sqrt{2}^\ldots}}$?
Problem:
How we can strictly prove $-\sqrt{2}^{-\sqrt{2}^{-\sqrt{2}^\ldots}}$ can't be 2?
Can $-\sqrt{2}^{-\sqrt{2}^{-\sqrt{2}^\ldots}}$ have the value expressed by complex numbers? (See below, in ...
39
votes
4answers
2k views
Are the solutions of $x^{x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}}}=2$ correct?
Problem:
Find $x$ in
$$\large x^{x^{x^{x^{ \cdot^{{\cdot}^{\cdot}} }}}}=2$$
Trick:
$x^{x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}}}=2$, so,
$x^{(x^{x^{x^{\cdot^{{\cdot}^{\cdot}}}}})}=x^2=2$, and,
...
2
votes
1answer
90 views
How to solve $x^x=k$? [duplicate]
Possible Duplicate:
$x^x=y$. How to solve for $x$?
If we have $x^x=4$ it's easily solved by substituting $x$ with $2$. But for general equation like $x^x = k$, how we can find the solution?
...
1
vote
0answers
117 views
What is the exact definition of a rational power?
I was taught in school that
$$x^{a/b} = \sqrt[b]{x^a}$$
however, wolfram says this is not always true:
$\sqrt[3]{x^2} \ne x^{2/3}$
...
2
votes
0answers
84 views
Finding the value of $x$ for an equation
If we have the expression $a=x^{c\cdot x+1}$ where the values of $a,c$ are known, how can we find the value of $x$?
I tried using log but it yields: $x = a ^ {(1/x)/(c-1/x)}$ from which I can't find ...
2
votes
1answer
172 views
Calculating the rightmost digits of Graham's number
Through some miscellaneous reading I have stumbled upon Graham's number and more precisely, a method of calculating the $d$ rightmost digits of the number. The exact method of calculation seems ...
24
votes
3answers
1k views
