Thread: monotonous decreasing function

May I call "log1/3n as a monotonous decreasing function?(1/3 is the base)
According to the book it is not. According to me it is.
it becomes -( logn/log3) and it decreases as n changes.

I can't write some symbols. an+1-an<0

Yes, $\displaystyle log_{1/3}(x)= -\frac{log(x)}{3}$ is a monotone, decreasing function.

More generally, $\displaystyle log_a(x)$ is monotone increasing if a> 1, monotone decreasing for 0< a< 1.

I believe you mean "monotonic"

In English "monotonous" means boring.

$\ln\left(\dfrac {1}{3n}\right)$ is monotonic for $n\geq 1$

I can't imagine why your book says it is not.

Many Thanks.

Originally Posted by romsek

$\ln\left(\dfrac {1}{3n}\right)$ is monotonic for $n\geq 1$

I can't imagine why your book says it is not.

It's not that expression. The OP stated that 1/3 is the base, not part of the argument.

Originally Posted by kastamonu

May I call "log1/3n as a monotonous decreasing function?(1/3 is the base)
According to the book it is not. According to me it is.
it becomes -( logn/log3) and it decreases as n changes.

I can't write some symbols. an+1-an<0

Maybe your book just means the function is not boring!