Log Functions Video Lecture | Physics for JEE Main & Advanced

Ans. A logarithm is the inverse operation of an exponential function. It is used to determine the exponent to which a base must be raised to obtain a given number. In other words, if we have an equation in the form y = b^x, the logarithm function allows us to find x when we know y and b. It is expressed as log base b of y.

Ans. Logarithmic functions have several properties. Some of the key properties include: - The logarithm of a product is equal to the sum of the logarithms of the individual factors: log(xy) = log(x) + log(y) - The logarithm of a quotient is equal to the difference of the logarithms of the individual terms: log(x/y) = log(x) - log(y) - The logarithm of a power is equal to the product of the exponent and the logarithm of the base: log(x^a) = a * log(x)

Ans. To solve logarithmic equations, we can use the properties of logarithms and algebraic manipulations. Here are the general steps: 1. Simplify the equation using properties of logarithms. 2. Isolate the logarithmic term on one side of the equation. 3. Convert the logarithmic equation into an exponential equation. 4. Solve the exponential equation for the unknown variable. 5. Check the solution by substituting it back into the original logarithmic equation.

Ans. The domain of a logarithmic function is the set of all positive real numbers. This is because logarithms are only defined for positive values. The range of a logarithmic function depends on the base of the logarithm. If the base is greater than 1, the range includes all real numbers. If the base is between 0 and 1, the range is limited to negative values.

Ans. Logarithmic functions are used in various real-life applications, including: - Finance: Logarithmic functions are used in financial calculations such as compound interest, stock market analysis, and calculating investment returns. - Science and engineering: Logarithmic functions are used in scientific research, engineering calculations, and data analysis to model exponential growth or decay. - Sound and music: Logarithmic functions are used in music theory to analyze and understand sound frequencies and create musical scales. - pH scale: The pH scale, used to measure the acidity or alkalinity of a substance, is based on logarithmic functions. Each unit change on the pH scale represents a tenfold change in acidity or alkalinity.