log18 3, log163 3, log1458 3 are in (a) AP (b) GP (c) HP (d) None of these

Name: Problem 164, Chapter 5: IIT-JEE Super Course in Mathematics
Uploaded: 2021-09-10T12:04:08-08:00
Duration: 2 min 17 s
Channel: Gaurav Kalra
Description: log18 3, log163 3, log1458 3 are in (a) AP (b) GP (c) HP (d) None of these

step 1 I have to check the given expressions here are in AP, GP, HP, or what? Let's look at that. So le

Log18 3, log163 3, log1458 3 are in (a) AP (b) GP (c) HP (d)...

Key Concepts

Harmonic Progression (HP)

A harmonic progression is a sequence of numbers whose reciprocals form an arithmetic progression. This means the sequence itself has a non-linear structure that can often be examined by considering the linearity of its reciprocal values.

Arithmetic Progression (AP)

An arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. This linear structure is characterized by its simplicity and the uniform interval between consecutive terms.

Geometric Progression (GP)

A geometric progression is a sequence where each term is obtained by multiplying the previous term by a constant non-zero factor, known as the common ratio. This exponential pattern is useful in modeling situations of growth and decay.

Logarithm

A logarithm represents the power to which a given base must be raised to obtain a specific value. This concept is fundamental in converting multiplicative operations into additive ones, which simplifies many types of calculations, and it helps solve problems involving exponential relationships.

Change-of-base Formula

The change-of-base formula allows a logarithm of any base to be rewritten in terms of logarithms with a different base, typically one that is more convenient for computation or comparison. This property is especially useful when dealing with logarithms that have different bases in order to standardize the expressions.

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