Question
Solve the equation
Solve for x
x=−1
Evaluate
log2(3−x)+log2(−x)=2
Find the domain
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Evaluate
{3−x>0−x>0
Calculate
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Evaluate
3−x>0
Move the constant to the right side
−x>0−3
Removing 0 doesn't change the value,so remove it from the expression
−x>−3
Change the signs on both sides of the inequality and flip the inequality sign
x<3
{x<3−x>0
Change the signs on both sides of the inequality and flip the inequality sign
{x<3x<0
Find the intersection
x<0
log2(3−x)+log2(−x)=2,x<0
Add the terms
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Evaluate
log2(3−x)+log2(−x)
Use logax+logay=logaxy to transform the expression
log2((3−x)(−x))
Multiply the terms
log2(−x(3−x))
log2(−x(3−x))=2
Convert the logarithm into exponential form using the fact that logax=b is equal to x=ab
−x(3−x)=22
Evaluate the power
−x(3−x)=4
Change the sign
x(3−x)=−4
Expand the expression
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Evaluate
x(3−x)
Apply the distributive property
x×3−x×x
Use the commutative property to reorder the terms
3x−x×x
Multiply the terms
3x−x2
3x−x2=−4
Move the expression to the left side
3x−x2−(−4)=0
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
3x−x2+4=0
Factor the expression
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Evaluate
3x−x2+4
Reorder the terms
−x2+3x+4
Rewrite the expression
−x2+(−1+4)x+4
Calculate
−x2−x+4x+4
Rewrite the expression
−x×x−x+4x+4
Factor out −x from the expression
−x(x+1)+4x+4
Factor out 4 from the expression
−x(x+1)+4(x+1)
Factor out x+1 from the expression
(−x+4)(x+1)
(−x+4)(x+1)=0
When the product of factors equals 0,at least one factor is 0
−x+4=0x+1=0
Solve the equation for x
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Evaluate
−x+4=0
Move the constant to the right-hand side and change its sign
−x=0−4
Removing 0 doesn't change the value,so remove it from the expression
−x=−4
Change the signs on both sides of the equation
x=4
x=4x+1=0
Solve the equation for x
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Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=4x=−1
Check if the solution is in the defined range
x=4x=−1,x<0
Solution
x=−1
Show Solution