Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x>2
Alternative Form
x∈(2,+∞)
Evaluate
log10(x3)>log10(2x×1)
Find the domain
More Steps
Evaluate
{x3>02x×1>0
The only way a base raised to an odd power can be greater than 0 is if the base is greater than 0
{x>02x×1>0
Calculate
More Steps
Evaluate
2x×1>0
Multiply the terms
2x>0
Rewrite the expression
x>0
{x>0x>0
Find the intersection
x>0
log10(x3)>log10(2x×1),x>0
Multiply the terms
log10(x3)>log10(2x)
For 10>1 the expression log10(x3)>log10(2x) is equivalent to x3>2x
x3>2x
Move the expression to the left side
x3−2x>0
Factor the expression
x(x2−2)>0
Separate the inequality into 2 possible cases
{x>0x2−2>0{x<0x2−2<0
Solve the inequality
More Steps
Evaluate
x2−2>0
Move the constant to the right side
x2>2
Take the 2-th root on both sides of the inequality
x2>2
Calculate
∣x∣>2
Separate the inequality into 2 possible cases
x>2x<−2
Find the union
x∈(−∞,−2)∪(2,+∞)
{x>0x∈(−∞,−2)∪(2,+∞){x<0x2−2<0
Solve the inequality
More Steps
Evaluate
x2−2<0
Move the constant to the right side
x2<2
Take the 2-th root on both sides of the inequality
x2<2
Calculate
∣x∣<2
Separate the inequality into 2 possible cases
{x<2x>−2
Find the intersection
−2<x<2
{x>0x∈(−∞,−2)∪(2,+∞){x<0−2<x<2
Find the intersection
x>2{x<0−2<x<2
Find the intersection
x>2−2<x<0
Find the union
x∈(−2,0)∪(2,+∞)
Check if the solution is in the defined range
x∈(−2,0)∪(2,+∞),x>0
Solution
x>2
Alternative Form
x∈(2,+∞)
Show Solution
