Logarithmic Equations and Inequalities

IMPORTANT

Logarithmic Equations and Inequalities: Overview

This topic covers concepts such as Logarithmic Function, Domain and Range of Logarithmic Function, Graph of Logarithmic Functions, Solving Logarithmic Equations, Solving Logarithmic Equations: with Constant Base, etc.

Important Questions on Logarithmic Equations and Inequalities

HARD
IMPORTANT

Consider the inequality logx151-2x<-2. Which of the following is/are CORRECT?

MEDIUM
IMPORTANT

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

HARD
IMPORTANT

If logyx+ logxy= y, then  x + y =

HARD
IMPORTANT

If  alogbx25xlogba+6=0 where a>0,b>0 &b1, then the value of x can be equal to

HARD
IMPORTANT

If 'x' is the solution of the equation

log3x+7 4x2+12x+9+log2x+36x2+23x+21=4,  then  1x2=

HARD
IMPORTANT

x1log3x22logx9=x17, then the value of x is

HARD
IMPORTANT

logx-14=1+log2x-1, then the values of x, will be

EASY
IMPORTANT

If log4log3log2x=0, then the value of x is.

HARD
IMPORTANT

91+logx-31+logx-210=0, then the value of x, is (where base of log is 3).

HARD
IMPORTANT

Let f be a function defined on the set of all positive integers such that fxy=fx+f(y) for all positive integers x, y. If f12=24 and f8=15 , the value of f48 is

HARD
IMPORTANT

If log2a+b+log2c+d4. Then the min. value of the expression a+b+c+d is

MEDIUM
IMPORTANT

The solution set of the inequality logcosx23-2x<logcosx22x-1 is

MEDIUM
IMPORTANT

Set of all the values of x satisfying the inequality logx+1xlog2x-1x+2>0 is

HARD
IMPORTANT

The least integer a, for which 1+log5x2+1log5ax2+4x+a is true for all xR is-

MEDIUM
IMPORTANT

Solution of the in equation log0.1log2x2+1x-1<0 contains the interval

EASY
IMPORTANT

The set of real values of x for which log0.2x+2x 1 is

EASY
IMPORTANT

If log0.04x-1log0.2x-1 then x belongs to the interval

EASY
IMPORTANT

The set of real values of x for which 2log2x-1>x+5 is

EASY
IMPORTANT

If log12sinx>0, x0, 4π, then the number of values of x, which are integral multiples of π4 is.