Como calcular logaritmos decimales, naturales y con base diferente con calculadora

What are logarithms used for in real life? From earthquakes to banks 📊 In this video, I'll explain how to calculate logarithms from scratch. We'll cover the three main types, with worked examples and real-world applications you'll actually use. What you'll learn today: Intro: What is a logarithm? Definition: A logarithm is the inverse of a power. If a raised to the power of y equals x, then the logarithm base a of x equals y. Conditions: a greater than zero and a not equal to 1. The 3 types of logarithms you should know 1. Base-10 logarithm or decimal logarithm How to write it: log of x without the base Easy examples: log of 100 equals 2, log of 1000 equals 3, log of 0.01 equals negative 2 Real-world applications: Earthquakes: The Richter scale uses base-10 logarithms. A magnitude 7 earthquake is 10 times stronger than a magnitude 6 earthquake. Chemistry: pH is calculated as pH equals negative log of the H+ ion concentration. pH 7 is neutral, pH 3 is acidic. 2. Natural or Napierian logarithm How to write it: ln of x. Its base is the number e, which is approximately 2.718. Examples with a calculator: ln of 1 equals 0, ln of e equals 1, ln of 10 is approximately 2.30. Real-world applications: Continuous compound interest: The formula uses e raised to the power of rt. Radioactive decay: Half-life with ln of 2. Population growth: Exponential models use ln to solve for time. 3. Logarithm of a base other than 10 Change of base formula: logarithm base a of x equals log of x divided by log of a. ln e x divided by ln of a also works. Examples: logarithm base 2 of 8 equals log of 8 divided by log of 2 equals 3. logarithm base 5 of 25 equals 2. Real-world applications: Computer science: Logarithms base 2 are used to measure algorithms. Example: Binary search is O of the base 2 log of n Financial Mathematics: To solve for time in compound interest, logarithms are used. Formula: t equals log (M/C) divided by n times log (1) plus i divided by n Practice Exercises Calculate these logarithms and leave your answer in the comments: 1. Base 10: log of 0.001 and log of 100,000 2. Natural: ln(e cubed) and ln(1/e) 3. Change of base: base 3 logarithm of 81 and base 4 logarithm of 2 4. Application: If an earthquake has a magnitude of 5.5, how many times more intense is it than one of 3.5? Key fact: Logarithms convert multiplications into additions. That's why NASA, banks, and your cell phone use them all the time. Subscribe for more applied math and leave your question below 👇 #Logarithms #Base10Logarithm #NaturalLogarithm #ChangeOfBase #Mathematics #Precalculus #Algebra #RichterScale #pH #CompoundInterest