Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
x>1
Alternative Form
x∈(1,+∞)
Evaluate
logx(2x×1)>1
Find the domain
More Steps
Evaluate
⎩⎨⎧x>02x×1>0x=1
Calculate
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Evaluate
2x×1>0
Multiply the terms
2x>0
Rewrite the expression
x>0
⎩⎨⎧x>0x>0x=1
Simplify
{x>0x=1
Find the intersection
x∈(0,1)∪(1,+∞)
logx(2x×1)>1,x∈(0,1)∪(1,+∞)
Multiply the terms
logx(2x)>1
Separate the inequality into 2 possible cases
logx(2x)>1,x>1logx(2x)>1,x<1
Calculate
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Evaluate
logx(2x)>1,x>1
For x>1 the expression logx(2x)>1 is equivalent to 2x>x
2x>x,x>1
Calculate
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Evaluate
2x>x
Add or subtract both sides
2x−x>0
Subtract the terms
x>0
x>0,x>1
x>0,x>1logx(2x)>1,x<1
Calculate
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Evaluate
logx(2x)>1,x<1
For x>1 the expression logx(2x)>1 is equivalent to 2x<x
2x<x,x<1
Calculate
More Steps
Evaluate
2x<x
Add or subtract both sides
2x−x<0
Subtract the terms
x<0
x<0,x<1
x>0,x>1x<0,x<1
Find the intersection
x>1x<0,x<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∈(0,1)∪(1,+∞)
Solution
x>1
Alternative Form
x∈(1,+∞)
Show Solution
