How far should I sum? How far should I sum?

The harmonic series is the "infinite sum" of all the fractions of the form \$\frac1n\$ for \$n\$ positive integer. I.e. the harmonic series is

$$\frac11 + \frac12 + \frac13 + \frac14 + \cdots$$

It is well-known that this sum diverges, which means that if you define

$$ H_n = \frac11 + \frac12 + \cdots + \frac1n$$

Then the value of \$H_n\$ goes to infinity. This can also be stated in a different way: for any positive value \$x\$ you pick, there is some value \$N\$ such that, to the right of \$N\$, the \$H\$ values are bigger than \$x\$:

$$\forall\ x\ \exists\ N: n &gt; N \implies H_n &gt; x $$

Your task

Write a program/function that takes as input a positive number x (not necessarily an integer) and outputs the first integer n for which

$$H_n \geq x$$

In theory your program must work for arbitrary x, even if in practice you are limited by the memory and/or precision of your programming language/computer.

Test cases

1.5 -&gt; 2
2 -&gt; 4
3 -&gt; 11
3.1415 -&gt; 13
4 -&gt; 31
5 -&gt; 83
7.5 -&gt; 1015
10 -&gt; 12367


This is code-golf so shortest solution wins! Standard loopholes are forbidden by default. Happy golfing.
APL (Dyalog), 13 bytes

-1 bytes thanks to ngn



{⊃⍸⍵≤+\÷⍳⌈*⍵}


Try it online!

A dfn solution that takes a right argument.

Explanation:

{           }   ⍝ dfn
 ⊃              ⍝ Take the first of
  ⍸             ⍝ The indexes of the truthy values of
   ⍵≤           ⍝ The right argument is smaller than or equal to
     \+         ⍝ The cumulative sum
       ÷        ⍝ The reciprocal of each of
        ⍳       ⍝ The range 1 to
         ⌈      ⍝ The ceiling of
          *⍵    ⍝ e to the power of the right argument