Tagged Questions
9
votes
1answer
308 views
Is the difference of the natural logarithms of two integers always irrational or 0?
If I have two integers $a,b > 1$. Is
$\ln(a) - \ln(b)$
always either irrational or $0$. I know both $\ln(a)$ and $\ln(b)$ are irrational.
3
votes
1answer
504 views
$\log_7 n$ is either an integer or an irrational number
Show that $\log_7 n$ is either an integer or an irrational number where n is a positive number.
I assumed that it is rational and tried to get a contradiction for $\log_7 n = a/b$, where b does ...
0
votes
1answer
417 views
About irrational logarithms
Could someone provide, please, a proof of the theorem below?
"Being x and b integers greater than 1, which can not be represented as powers of the same basis(positive integer) and integer exponent, ...
