Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x>1
Alternative Form
x∈(1,+∞)
Evaluate
ln(x)×x>0
Find the domain
ln(x)×x>0,x>0
Multiply the terms
xln(x)>0
Separate the inequality into 2 possible cases
{x>0ln(x)>0{x<0ln(x)<0
Solve the inequality
More Steps
Evaluate
ln(x)>0
For e>1 the expression ln(x)>0 is equivalent to x>e0
x>e0
Evaluate the power
x>1
{x>0x>1{x<0ln(x)<0
Solve the inequality
More Steps
Evaluate
ln(x)<0
For e>1 the expression ln(x)<0 is equivalent to x<e0
x<e0
Evaluate the power
x<1
{x>0x>1{x<0x<1
Find the intersection
x>1{x<0x<1
Find the intersection
x>1x<0
Find the union
x∈(−∞,0)∪(1,+∞)
Check if the solution is in the defined range
x∈(−∞,0)∪(1,+∞),x>0
Solution
x>1
Alternative Form
x∈(1,+∞)
Show Solution
