diff --git a/firstAndLastElementOfAnArr.js b/firstAndLastElementOfAnArr.js
new file mode 100644
index 00000000..f010fc8a
--- /dev/null
+++ b/firstAndLastElementOfAnArr.js
@@ -0,0 +1,57 @@
+/**
+ * @param {number[]} nums
+ * @param {number} target
+ * @return {number[]}
+ * 
+ * Intution: 
+ * The approach here is using binary search twice to get start and end index of the target
+ * We are even returning the firstFound location, so that we can optimize the end index calculation
+ * Time complexity is O(log n) + O(log n) => O(log n)
+ * 
+ */
+
+
+var searchRange = function (nums, target) {
+    let left = 0, right = nums.length - 1;
+    // Method to get the first occurence of the target
+    const firstLocBinarySearch = (low, high) => {
+        let firstFound = -1;
+        while (low <= high) {
+            const mid = Math.floor(low + (high - low) / 2);
+            if (nums[mid] === target) {
+                if (firstFound === -1) firstFound = mid;
+                if (mid === 0 || nums[mid] !== nums[mid - 1]) return [firstFound, mid];
+                else high = mid - 1;
+            } else if (nums[mid] < target) {
+                low = mid + 1;
+            } else {
+                high = mid - 1;
+            }
+        }
+        return [-1, -1];
+    }
+
+    // Method to get the last occurence of the target
+    const lastLocBinarySearch = (low, high) => {
+        while (low <= high) {
+            const mid = Math.floor(low + (high - low) / 2);
+            if (nums[mid] === target) {
+                if (mid === nums.length - 1 || nums[mid] !== nums[mid + 1]) return mid;
+                else low = mid + 1;
+            } else if (nums[mid] < target) {
+                low = mid + 1;
+            } else {
+                high = mid - 1;
+            }
+
+        }
+
+        return -1;
+    }
+    //  get the firstfound location and the startIndex
+    let [firstFound, startIndex] = firstLocBinarySearch(left, right);
+    // if firstFound is -1 then the element is not found, can ignore the remaining code and return [-1,-1]
+    if (firstFound === -1) return [-1, -1];
+    let endIndex = lastLocBinarySearch(startIndex, right);
+    return [startIndex, endIndex];
+};
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