# Tagged Questions

Questions about exponentiation, the operation of raising a base $b$ to an exponent $a$ to give $b^a$.

1answer
31 views

### $4^{3a-1}-5^{2b-3}=0$ find a in terms of $b$

If $4^{3a-1}-5^{2b-3}=0$ then find a using $b$. My Attempt:we know that $2^{6a-2}=5^{2b-3}$ with this way we can find a value for $a$ and $b$ if both sides are zero if we can find another value for ...
2answers
16 views

### Image: proof re fractional exponents

Can someone help me prove that $(a^m)^{1/n} = (a^{1/n})^m$ per the textbook excerpt captured in the image?
8answers
2k views

### Which of the numbers is larger: $7^{94}$ or $9^{91}$?

In this problem, I guess b is larger, but not know how to prove it without going to lengthy calculations. It is highly appreciated if anyone can give me a help. Which number is larger ...
3answers
3k views

### Trace of the matrix power

Say I have matrix $A = \begin{bmatrix} a & 0 & -c\\ 0 & b & 0\\ -c & 0 & a \end{bmatrix}$. What is matrix trace tr(A^200) Thanks much!
2answers
33 views

### log to exponential form, but with number in front of log

So I understand how to put a log equation into exponential form. For example, $y = \log_2(x)$ is $2^y = x.$ However, I don't understand what to do when there is a number in front of $\log$, such as ...
2answers
71 views

### $8^a=3$ and $3^b=5$ and $10^c=5$ then find $c$ in terms of $a$ and $b$.

if $8^a=3$ and $3^b=5$ and $10^c=5$ then find $c$ using $a$ and $b$. My Attempt: if $8^a=3$ and $3^b=5$ then we can say that $8^{ab}=5$ and then we have $2^{3ab}=10^c$ but i cant solve this ...
0answers
79 views

### Solving an equation with infinite exponents [closed]

How would I find the exact value of this infinite power tower? $$(1+2^{0})^{(1+2^{-1})^{(1+2^{-2})^{.^{.^{.}}}}}$$ I have found a decimal expansion of the number through calculation of the first few ...
1answer
37 views

### Exponential of a symmetric matrix

Let $A$ be a real, symmetric and positive definite matrix and suppose $B$ is a real symmetric matrix such that $\exp(B) = A$. Is $B$ unique? The solution of my homework sheet says that $B$ is ...
15answers
5k views

### math fallacy problem: $-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1$?

I know there is something wrong with this but I don't know where. It's some kind of a math fallacy and it is driving me crazy. Here it is: $$-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1?$$
1answer
28 views

### simple question, need help

Can someone tell me where does 1 come from on the end, this got me really confused.
1answer
41 views

0answers
40 views

### If $\log_510=\log_7x(\log_nm)$ then the values of x,m and n are?

I have the question that if $\log_510=\log_7x(\log_nm)$ then values of $x$,$m$ and $n$ are? This question looks easy but i tried to get the expression down to the form $$\log_ab=\log_ac\tag{1.}$$ and ...
1answer
27 views

### $\forall x,y\in \mathbb{R}\colon\forall n\in \mathbb{N}\colon [Odd(n)\lor Even(n) \land y\geq 0\implies [x^\frac{1}{n} =y\iff x=y^n ]]$ [closed]

Prove the following theorem : $\forall x,y\in \mathbb{R}\colon\forall n\in \mathbb{N}\colon [Odd(n)\lor Even(n) \land y\geq 0\implies [x^\frac{1}{n} =y\iff x=y^n ]]$ Thank you :)
2answers
65 views

### Simplify: $S=3^{1/3}\cdot 7^{1/4}$

Simplify: $$S=3^{1/3}\cdot7^{1/4}$$ How is it possible to simplify this? The exponents are completely different.
2answers
34 views

1answer
19 views

### negative fraction exponent and division

Quick question on how to handle negative fraction exponents when differentiating: I have this problem to differentiate. $$x^{2/3} + y^{2/3} = 1$$ So my textbook and I both did the first thing the ...