Mister Exam

Other calculators

Solving inequalities/ lgx<2

lgx<2 inequation

A inequation with variable

The solution

You have entered [src] 
log(x) < 2
log⁡(x)<2\log{\left(x \right)} < 2 
log(x) < 2
Detail solution
Given the inequality:
log⁡(x)<2\log{\left(x \right)} < 2
To solve this inequality, we must first solve the corresponding equation:
log⁡(x)=2\log{\left(x \right)} = 2
Solve:
Given the equation
log⁡(x)=2\log{\left(x \right)} = 2
log⁡(x)=2\log{\left(x \right)} = 2
This equation is of the form:
log(v)=p

By definition log
v=e^p

then
x=e21x = e^{\frac{2}{1}}
simplify
x=e2x = e^{2}
x1=e2x_{1} = e^{2}
x1=e2x_{1} = e^{2}
This roots
x1=e2x_{1} = e^{2}
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
x0<x1x_{0} < x_{1}
For example, let's take the point
x0=x1−110x_{0} = x_{1} - \frac{1}{10}
=
−110+e2- \frac{1}{10} + e^{2}
=
−110+e2- \frac{1}{10} + e^{2}
substitute to the expression
log⁡(x)<2\log{\left(x \right)} < 2
log⁡(−110+e2)<2\log{\left(- \frac{1}{10} + e^{2} \right)} < 2
   /  1     2\    
log|- -- + e | < 2
   \  10     /

the solution of our inequality is:
x<e2x < e^{2}
 _____          
      \    
-------ο-------
       x1
Solving inequality on a graph
05-10-510152025-1010
Rapid solution 2 [src] 
     2 
(0, e )
x in (0,e2)x\ in\ \left(0, e^{2}\right) 
x in Interval.open(0, exp(2))
Rapid solution [src] 
   /            2\
And\0 < x, x < e /
0<x∧x<e20 < x \wedge x < e^{2} 
(0 < x)∧(x < exp(2))
    © Mister Exam – Calculator