Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
−1−log2(23)+1<x<1−log2(23)+1
Alternative Form
x∈−1−log2(23)+1,1−log2(23)+1
Evaluate
(21)x2−2x>23
Take the logarithm of both sides
log21((21)x2−2x)<log21(23)
Evaluate the logarithm
x2−2x<log21(23)
Move the expression to the left side
x2−2x−log21(23)<0
Subtract the terms
More Steps
Evaluate
x2−2x−log21(23)
Simplify
More Steps
Evaluate
log21(23)
Write the number in exponential form with the base of 2
log2−1(23)
Rewrite the logarithm
−log2(23)
x2−2x−(−log2(23))
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x2−2x+log2(23)
x2−2x+log2(23)<0
Move the constant to the right side
x2−2x<0−log2(23)
Add the terms
x2−2x<−log2(23)
Add the same value to both sides
x2−2x+1<−log2(23)+1
Evaluate
x2−2x+1<1−log2(23)
Evaluate
(x−1)2<1−log2(23)
Take the 2-th root on both sides of the inequality
(x−1)2<1−log2(23)
Calculate
∣x−1∣<1−log2(23)
Separate the inequality into 2 possible cases
⎩⎨⎧x−1<1−log2(23)x−1>−1−log2(23)
Calculate
⎩⎨⎧x<1−log2(23)+1x−1>−1−log2(23)
Calculate
⎩⎨⎧x<1−log2(23)+1x>−1−log2(23)+1
Solution
−1−log2(23)+1<x<1−log2(23)+1
Alternative Form
x∈−1−log2(23)+1,1−log2(23)+1
Show Solution
