Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
0<x<6
Alternative Form
x∈(0,6)
Evaluate
2log10(x×1)−2log10(6)<0
Find the domain
More Steps
Evaluate
x×1>0
Any expression multiplied by 1 remains the same
x>0
2log10(x×1)−2log10(6)<0,x>0
Simplify
More Steps
Evaluate
2log10(x×1)−2log10(6)
Any expression multiplied by 1 remains the same
2log10(x)−2log10(6)
Rewrite the expression
log10(x)×2−log10(6)×2
Factor the expression
(log10(x)−log10(6))×2
Use logax−logay=logayx to transform the expression
log10(6x)×2
Multiply the terms
2log10(6x)
2log10(6x)<0
Rewrite the expression
log10(6x)<0
For 10>1 the expression log10(6x)<0 is equivalent to 6x<100
6x<100
Evaluate the power
6x<1
Cross multiply
x<6
Check if the solution is in the defined range
x<6,x>0
Solution
0<x<6
Alternative Form
x∈(0,6)
Show Solution
