Problem No.3 Based on Value of Function - Functions - Diploma Maths - II

TL;DR

This video explains how to solve a mathematical problem involving logarithmic properties and provides step-by-step instructions.

Transcript

Click the bell icon to get latest videos from EKeeda Hi friends in this video we are going to see problem number 3 which is based on value of function now the Sun goes if f of X is equal to 16 raised to X plus log X to the base for find f of 1 by 2 now to solve this sum we need some basic properties which are related to logarithm so first property ... Read More

Key Insights

• 🧑‍💻 Logarithmic properties, such as log of e raised to M is M log E, log of a plus log of B is equal to log A multiplied by B, and log E to the base a is equal to 1, are essential in solving logarithmic equations.
• 😑 To find the value of f(1/2) in a given function, the expression is simplified by replacing X with 1/2 and applying logarithmic properties.
• 🫚 The value of the square root of 16 is 4, which is utilized in the calculation.
• 🧑‍💻 The formula log a to the base b equals log a divided by log b is used to find the value of log 2 to the base 4.

Questions & Answers

Q: What are the three basic properties of logarithms mentioned in the video?

The three properties are: log of e raised to M is M log E, log of a plus log of B is equal to log A multiplied by B, and log E to the base a is equal to 1. These properties are essential in solving logarithmic equations.

Q: How is the value of f(1/2) calculated in the given function?

To find f(1/2), we replace X with 1/2 in the function f(X) = 16^X + log(X) to the base 4. By simplifying the expression using the properties of logarithms, the value is computed as 7/2.

Q: How is the square root of 16 expressed in the calculation?

The square root of 16 is expressed as 4 in the calculation. This is because 16 raised to the power of 1/2 is equivalent to the square root of 16.

Q: What is the formula used to find the value of log 2 to the base 4?

The formula used is log 2 to the base 4 equals log 2 divided by log 4. This formula, log a to the base b equals log a divided by log b, is utilized to simplify the expression and calculate the value.

Summary & Key Takeaways

• The video introduces three basic properties related to logarithms: log of e raised to M is M log E, log of a plus log of B is equal to log A multiplied by B, and log E to the base a is equal to 1.

• The problem in focus is finding the value of f(1/2) in the given function f(X) = 16^X + log(X) to the base 4.

• By applying the properties mentioned earlier, the video demonstrates the process of solving the problem step by step.

• The final value of the expression is calculated to be 7/2.