(-2)^x = - 1/128
solve for x
5 answers
does x=-7?
yes
Your answer is correct.
( - 2 )ˣ = - 1 / 128
Multiply both sides by 128
128∙( - 2 )ˣ = - 1
Raise both sides to the power 2
128²∙[ ( - 2 )² ]ˣ = ( - 1 )²
128 = 2⁷ , ( - 2 )² = ( 2 )² , so:
(2⁷)²∙(2²)ˣ = 1
_______________________________
Remark:
(2⁷)² is the same (2²)⁷
___________________________
(2²)⁷∙(2²)ˣ = 1
4⁷∙4ˣ = 1
_____________________
Remark:
nᵃ∙ nᵇ = nᵃ⁺ᵇ
Any number raised to the powe zero is one.
So:
4⁷ ∙ 4ˣ = 4⁷⁺ˣ
4⁰ = 1
_____________________
4⁷⁺ˣ = 4⁰
Take the logarithms base 4 of both sides
log₄( 4⁷⁺ˣ ) = log₄( 4⁰ )
_______________________________________
Remark:
log aᵐ = m ∙ log a
log₄( 4 ) = 1
So:
log₄( 4⁷⁺ˣ ) = ( 7 + x ) ∙ log₄ ( 4 ) = ( 7 + x ) ∙ 1 = 7 + x
log₄= 4⁰ = 0 ∙ log₄( 4 ) = 0
_______________________________________
7 + x = 0
Subtract 7 to both sides
7 + x - 7 = 0 - 7
x = - 7
( - 2 )ˣ = - 1 / 128
Multiply both sides by 128
128∙( - 2 )ˣ = - 1
Raise both sides to the power 2
128²∙[ ( - 2 )² ]ˣ = ( - 1 )²
128 = 2⁷ , ( - 2 )² = ( 2 )² , so:
(2⁷)²∙(2²)ˣ = 1
_______________________________
Remark:
(2⁷)² is the same (2²)⁷
___________________________
(2²)⁷∙(2²)ˣ = 1
4⁷∙4ˣ = 1
_____________________
Remark:
nᵃ∙ nᵇ = nᵃ⁺ᵇ
Any number raised to the powe zero is one.
So:
4⁷ ∙ 4ˣ = 4⁷⁺ˣ
4⁰ = 1
_____________________
4⁷⁺ˣ = 4⁰
Take the logarithms base 4 of both sides
log₄( 4⁷⁺ˣ ) = log₄( 4⁰ )
_______________________________________
Remark:
log aᵐ = m ∙ log a
log₄( 4 ) = 1
So:
log₄( 4⁷⁺ˣ ) = ( 7 + x ) ∙ log₄ ( 4 ) = ( 7 + x ) ∙ 1 = 7 + x
log₄= 4⁰ = 0 ∙ log₄( 4 ) = 0
_______________________________________
7 + x = 0
Subtract 7 to both sides
7 + x - 7 = 0 - 7
x = - 7
whoa! Can you say overkill??
Steve
solve for x mean SOLVE for x
Just say:
x = - 7 is not enough.
I showed the way to the solution.
solve for x mean SOLVE for x
Just say:
x = - 7 is not enough.
I showed the way to the solution.