Given the number N, the task is to find the cube root using the log function.
Examples:
Input: N = 8
Output: 2.000000
Input: N = 27
Output: 3.000000
Approach: To solve the problem mentioned above we will use log() function, according to the following formula:
Let cube root of N be d.
=> ?N = d
=> N(1/3) = d
Now, apply log on both sides:
log3 (N(1/3)) = log3 (d)
=> log3 (d) = 1/3 * log3 (N)
=> d = 3(1/3 * log3 (N))
Below is the implementation of the above problem:
C++
// C++ program to Find Cube root// of a number using Logarithm#include <bits/stdc++.h>// Function to find the cube rootdouble cubeRoot(double n){ // calculate the cube root double ans = pow(3, (1.0 / 3) * (log(n) / log(3))); // Return the final answer return ans;}// Driver codeint main(){ double N = 8; printf("%.2lf ", cubeRoot(N)); return 0;} |
Java
// Java program to Find Cube root// of a number using Logarithmclass GFG{ // Function to find the cube rootstatic double cubeRoot(double n){ // Calculate the cube root double ans = Math.pow(3, ((1.0 / 3) * (Math.log(n) / Math.log(3)))); // Return the final answer return ans;}// Driver codepublic static void main(String[] args){ double N = 8; System.out.printf("%.2f", cubeRoot(N));}}// This code is contributed by Rajput-Ji |
Python3
# Python3 program to find cube root # of a number using logarithm import numpy as np# Function to find the cube root def cubeRoot(n): # Calculate the cube root ans = pow(3, (1.0 / 3) * (np.log(n) / np.log(3))) # Return the final answer return ans # Driver codeN = 8print("%.2f" % cubeRoot(N))# This code is contributed by PratikBasu |
C#
// C# program to find cube root// of a number using logarithmusing System;class GFG{ // Function to find the cube rootstatic double cubeRoot(double n){ // Calculate the cube root double ans = Math.Pow(3, ((1.0 / 3) * (Math.Log(n) / Math.Log(3)))); // Return the readonly answer return ans;}// Driver codepublic static void Main(String[] args){ double N = 8; Console.Write("{0:F2}", cubeRoot(N));}}// This code is contributed by sapnasingh4991 |
Javascript
<script>// javascript program to Find Cube root// of a number using Logarithm// Function to find the cube rootfunction cubeRoot( n){ // calculate the cube root let ans = Math.pow(3, (1.0 / 3) * (Math.log(n) / Math.log(3))); // Return the final answer return ans;}// Driver codelet N = 8;document.write( cubeRoot(N).toFixed(2)); // This code is contributed by todaysgaurav </script> |
Output
2.00
Time complexity: O(log2(log3n))
Auxiliary space: O(1)
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