Logarithms - Basics Video Lecture | Logarithms Simplified (Mathematics Trick): Important for K12 students - Quant

Ans. A logarithm is a mathematical function that represents the exponent to which a base must be raised to obtain a given number. In other words, it is the inverse operation of exponentiation. For example, in the equation 10^2 = 100, the logarithm (base 10) of 100 is 2.

Ans. Logarithms help in solving exponential equations by simplifying equations that involve exponential terms. By taking the logarithm of both sides of an exponential equation, the equation can be transformed into a simpler form where the variable is isolated. This allows us to solve for the variable using basic algebraic techniques.

Ans. The properties of logarithms include the product rule, quotient rule, power rule, and change of base rule. - The product rule states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. - The quotient rule states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. - The power rule states that the logarithm of a number raised to a power is equal to the product of the exponent and the logarithm of the base. - The change of base rule allows us to calculate logarithms in different bases using logarithms in a known base.

Ans. Logarithms are used in various real-life applications, including: - pH scale: The pH scale, which measures the acidity or alkalinity of a solution, is based on logarithms. Each unit on the pH scale represents a tenfold difference in acidity or alkalinity. - Sound intensity: The decibel scale, used to measure the intensity of sound, is logarithmic. Each increase of 10 decibels represents a tenfold increase in sound intensity. - Richter scale: The Richter scale, used to measure the magnitude of earthquakes, is logarithmic. Each increase of one unit on the Richter scale represents a tenfold increase in the amplitude of seismic waves.

Ans. Logarithms can only be calculated for positive numbers. It is not possible to take the logarithm of a negative number or zero. This is because the logarithm function is only defined for positive values. When working with logarithms, it is important to ensure that the argument (the number inside the logarithm) is always greater than zero.