Logarithm Laws Video Lecture | Mathematics (Maths) for JEE Main & Advanced

Ans. The basic logarithm laws in JEE 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 power and the logarithm of the number. The change of base rule states that the logarithm of a number with one base can be expressed as the logarithm of the same number with a different base by dividing the logarithm of the number with the old base by the logarithm of the new base.

Ans. Logarithm laws help in simplifying complex expressions in JEE by allowing us to manipulate logarithmic functions and convert them into simpler forms. These laws enable us to break down logarithms of products or quotients into sums or differences of logarithms, respectively, which can often lead to cancellation of terms or simplification of the expression. The power rule allows us to bring down exponents as coefficients, facilitating further simplification. The change of base rule helps in converting logarithms with one base to logarithms with a different base, which can be more easily evaluated or manipulated algebraically.

Ans. The product rule of logarithms can be applied in JEE problems by using the property that the logarithm of a product is equal to the sum of the logarithms of the individual factors. This means that if we have the logarithm of a product, we can split it into the sum of logarithms of the individual factors. This property can be particularly useful in simplifying expressions involving products of variables or functions. By applying the product rule, we can often break down complex expressions into simpler ones, making them easier to work with and evaluate.

Ans. The quotient rule of logarithms helps in solving equations in JEE by allowing us to simplify expressions involving logarithms of quotients. The quotient rule states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. By applying this rule, we can convert logarithms of quotients into differences of logarithms, which can often lead to cancellation of terms or simplification of the expression. This simplification can make it easier to solve logarithmic equations, as it reduces the complexity of the expressions involved.

Ans. The change of base rule should be used in JEE problems when we need to evaluate logarithms with bases that are not easily calculable or manipulate logarithmic expressions algebraically. The change of base rule allows us to convert logarithms with one base to logarithms with a different base by dividing the logarithm of the number with the old base by the logarithm of the new base. This can be particularly useful when we want to evaluate logarithms using a calculator that only supports certain bases, such as base 10 or base e (natural logarithm). Additionally, the change of base rule can help in simplifying expressions or performing algebraic manipulations involving logarithms with different bases.