logarithm question

[hollow geyser]

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[lusty spruce]

,rotate

[lusty spruce]

You can show that $\prod_{d\mid n}d=n^{\tau(n)/2}$, where $\tau(n)$ counts the number of divisors

[ornate ridge]

Omegabet_

[lusty spruce]

to which you get an explicit value of x

[chilly parcel]

yeah I saw this formula just today

But

this question can be solved without the formula

[lusty spruce]

I assume it can be

[chilly parcel]

that's what I'm looking for

[lusty spruce]

ig argue how many divisors are between 1 and 10, 10 and 100, 100 and 1000,...?

[chilly parcel]

What will that achieve

[lusty spruce]

lets you determine what integers x lies between I believe

[lusty spruce]

I mentioned this cause this is how I would attempt it. I dont readily see another way

[mortal crag]

@chilly parcel do you know the formula for number of divisors of a particular number?

[faint yacht]

all positive divisors of a number n ranges between 1 to sqrt(n)

so in your case you just need to check up to 10⁴