Answer:
The value of x is -14.
Step-by-step explanation:
Given : 81⁻⁴ ÷ 729²⁻ˣ = 9⁴ˣ
This can be written as \frac{81^{-4} }{729^{2-x} }7292−x81−4 = 9⁴ˣ
In order to solve this, we have to convert them to the same base.
We know that 9² = 81 and 9³ = 729. Therefore,
=> \frac{(9^{2}) ^{-4} }{(9^{3})^{2-x} }(93)2−x(92)−4 = 9⁴ˣ
=> \frac{9^{-8} }{9^{6-3x} }96−3x9−8 = 9⁴ˣ (because (x^{n})^{m} = x^{nm}(xn)m=xnm )
=> 9^{-8-(6-3x)}9−8−(6−3x) = 9⁴ˣ (because \frac{x^{n}}{x^{m}} = x^{n-m}xmxn=xn−m )
=> 9^{-8-6+3x}9−8−6+3x = 9⁴ˣ
=> 9^{-14+3x}9−14+3x = 9⁴ˣ
As the base is same on both the left and right hand side, the exponents can be equated.
=> -14 + 3x = 4x
=> 3x - 4x = 14
=> -x = 14
=> x = -14
Therefore, the value of x is -14.
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Answers & Comments
Answer:
The value of x is -14.
Step-by-step explanation:
Given : 81⁻⁴ ÷ 729²⁻ˣ = 9⁴ˣ
This can be written as \frac{81^{-4} }{729^{2-x} }7292−x81−4 = 9⁴ˣ
In order to solve this, we have to convert them to the same base.
We know that 9² = 81 and 9³ = 729. Therefore,
=> \frac{(9^{2}) ^{-4} }{(9^{3})^{2-x} }(93)2−x(92)−4 = 9⁴ˣ
=> \frac{9^{-8} }{9^{6-3x} }96−3x9−8 = 9⁴ˣ (because (x^{n})^{m} = x^{nm}(xn)m=xnm )
=> 9^{-8-(6-3x)}9−8−(6−3x) = 9⁴ˣ (because \frac{x^{n}}{x^{m}} = x^{n-m}xmxn=xn−m )
=> 9^{-8-6+3x}9−8−6+3x = 9⁴ˣ
=> 9^{-14+3x}9−14+3x = 9⁴ˣ
As the base is same on both the left and right hand side, the exponents can be equated.
=> -14 + 3x = 4x
=> 3x - 4x = 14
=> -x = 14
=> x = -14
Therefore, the value of x is -14.
Step-by-step explanation:
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