<p>Log : <input id="a" type="text"/>(<input id="b" type="text"/>)= <label id="result"></label></p>
<button onClick="logCalc()">validé</button>
<script>
  function logCalc(){
    let a = document.querySelector('#a').value;
    let b = document.querySelector('#b').value;
    document.querySelector('#result').innerHTML = Math.log(a) / Math.log(b);
  }
</script>

<input type="text" id="decimal" />
<button type="button" onClick="decimal2fraction()">Calculer</button>
<label id="result">...</label>
<script>
  function decimal2fraction() {
    var value = document.querySelector('#decimal').value;
    var best_number = 1;
    var best_denom = 1;
    var best_err = Math.abs(value - best_number / best_denom);
    for (var denom = 1; denom <= 10000; denom++) {
      var number = Math.round(value * denom);
      var err = Math.abs(value - number / denom);
      if (err < best_err) {
        best_number = number;
        best_denom = denom;
        best_err = err;
        document.querySelector("#result").innerText = "result : " + best_number + " / " + best_denom + " = " + (best_number / best_denom);
      }
    }
  }
</script>