Logarithmic Equations and Inequalities

IMPORTANT

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

MEDIUM
IMPORTANT

Let n be the smallest positive integer such that 1+12+13++1n4. Which one of the following statements is true?

HARD
IMPORTANT

The number of integers satisfying the inequality log0.9 log5x2+5+x>0 is:

HARD
IMPORTANT

Number of integral solutions of inequality 110logx-3x2-4x+31 are 

EASY
IMPORTANT

If log2x=13.log28-2log23, then x is equal to

EASY
IMPORTANT

If logelog52x-2+3=0 then the value of x is-

EASY
IMPORTANT

The number of solutions of the equation, log-2x=logx2 is

HARD
IMPORTANT

Number of integers satisfying inequality, log3x-1+12log3x3log313+2>0 is

MEDIUM
IMPORTANT

Number of real values of x which satisfy log2x2+log2x+2=4 is/are

EASY
IMPORTANT

Let fx=log 2x-12x3+3x2+x, then domain of fx contain the set

EASY
IMPORTANT

If 1-log105=13log1012+log10x+13log105 then x is equal to

EASY
IMPORTANT

A controlled experiment took place in a laboratory. Biologists estimated the number of microbes N present in a culture t days after the start of their experiment. The first results obtained are shown in the top two rows of the table below.

t35101520N1151784809001600logN

Complete the last row of the table, giving values to 2 decimal places.

Draw a graph of logN against t, using appropriate  scales.

EASY
IMPORTANT

log8+log8x2+x-2=43 ,  then x is equal to-

HARD
IMPORTANT

Solution of inequality loglog2x2x2-10x+22>0 is

MEDIUM
IMPORTANT

Prove that the value of log103 lies in between 12 and 25.

MEDIUM
IMPORTANT

Prove that the value of log103 lies in between 12 and 25.

MEDIUM
IMPORTANT

Let x, y be real numbers such that x>2y>0 and 2logx-2y=logx+logy. Then the possible value(s) of xy

MEDIUM
IMPORTANT

Find the domain of the function fx=log4(4x-3).

MEDIUM
IMPORTANT

Find the domain of the function fx=log4(2x-3).

HARD
IMPORTANT

The set of numeric values of x which satisfy the equation logx2x2-10 is