Logarithmic Equations and Inequalities
Logarithmic Equations and Inequalities: Overview
This topic covers concepts, such as, Domain & Range of Logarithmic Function, Graph of Logarithmic Functions, Solving Logarithmic Equations: with Variable Base & Solving Logarithmic Inequalities: with Variable Base etc.
Important Questions on Logarithmic Equations and Inequalities
Let be the smallest positive integer such that . Which one of the following statements is true?

The number of integers satisfying the inequality is:

Number of integral solutions of inequality are

If , then is equal to

If then the value of is-

The number of solution of the equation, is

Number of integers satisfying inequality, is

Number of real values of which satisfy is/are

Let , then domain of contain the set

If then is equal to

A controlled experiment took place in a laboratory. Biologists estimated the number of microbes present in a culture days after the start of their experiment. The first results obtained are shown in the top two rows of the table below.
Complete the last row of the table, giving values to decimal places.
Draw a graph of against , using appropriate scales.

Solve

then is equal to-

Solution of inequality is

Prove that the value of lies in between and .

Prove that the value of lies in between and .

Let be real numbers such that and . Then the possible value(s) of

Find the domain of the function .

Find the domain of the function .

The set of numeric values of which satisfy the equation is
