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JEE Main Previous Year Questions (2026): Logarithms
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Page 1 JEE Main Previous Year Questions (2025): Logarithms Q1: The product of all solutions of the equation ?? ?? ( ???? ?? ?? ?? ) ?? + ?? = ?? ?? , ?? > ?? , is : (A) ?? 2 (B) ?? (C) ?? 6 5 (D) e 8 / 5 Ans: (D) Solution: We begin with the equation: ?? 5 ( l og ?? ? ?? ) 2 + 3 = ?? 8 , ?? > 0 Equating the exponents, we have: 5 ( log ?? ? ?? ) 2 + 3 = log ?? ? ?? 8 = 8 log ?? ? ?? Let ?? = log ?? ? ?? . Substituting, the equation becomes: 5 ?? 2 + 3 = 8 ?? Rewriting this as a quadratic equation: 5 ?? 2 - 8 ?? + 3 = 0 Factoring the quadratic: 5 ?? 2 - 5 ?? - 3 ?? + 3 = 0 ? ( 5 ?? - 3 ) ( ?? - 1 ) = 0 Thus, the solutions for ?? are: ?? = 1 implies log ?? ? ?? = 1, giving ?? = ?? . ?? = 3 5 implies log ?? ? ?? = 3 5 , giving ?? = ?? 3 5 . The product of all solutions is: ?? 1 × ?? 3 5 = ?? 1 + 3 5 = ?? 8 5Read More
FAQs on JEE Main Previous Year Questions (2026): Logarithms
| 1. What are logarithms and why are they important in mathematics? |  |
Ans.Logarithms are the inverse operations of exponentiation. They express the power to which a number (the base) must be raised to obtain another number. For example, if b^y = x, then log_b(x) = y. Logarithms are important in mathematics because they simplify complex calculations, especially in areas like algebra, calculus, and exponential growth or decay models.
| 2. How do you solve logarithmic equations? | |
Ans.To solve logarithmic equations, you can use the properties of logarithms such as the product, quotient, and power rules. First, isolate the logarithmic term. Then, rewrite the equation in exponential form. Finally, solve for the variable. For instance, if log_b(x) = y, you can rewrite it as x = b^y and solve for x.
| 3. What are the common bases used in logarithms? | |
Ans.The most common bases used in logarithms are 10 (common logarithm, denoted as log(x) or log₁₀(x)) and e (natural logarithm, denoted as ln(x)). Base 2 is also frequently used in computer science. Each base serves a specific purpose, with base 10 often used for scientific calculations and base e for continuous growth models.
| 4. Can you explain the change of base formula for logarithms? | |
Ans.The change of base formula allows you to convert logarithms from one base to another. It states that log_b(a) = log_k(a) / log_k(b) for any positive base k. This is useful when calculating logarithms on calculators that only support certain bases, allowing you to switch to a more convenient base.
| 5. What are some real-world applications of logarithms? | |
Ans.Logarithms have numerous real-world applications, including in fields such as science, engineering, and finance. They are used in calculating pH in chemistry, measuring earthquake intensity on the Richter scale, and analyzing exponential growth in populations. Additionally, logarithmic scales help in simplifying the representation of large numbers, such as in music (decibels) and data compression.
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