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opgqwav8w1m
@opgqwav8w1m
August 2022
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Показательное неравенство[tex] \frac{30* 5^{x+3} - 0,2^{x+1} }{ 5^{3-x}- 25^{1-x} } \geq 5^{x-3} [/tex]
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oganesbagoyan
Verified answer
(
30*5^(x+3) -0,2^(x+1)
) /(
5^(3-x) -25^(1-x)
)
≥5^(x-3) ;
(
30*5^(x+3) -5^(-x-1)
) /(
5^(3-x) -5^(2-2x)
)
≥5^(x-3) ;
(
30*5^(x+3) -5^(-x-1)
) /(
5^(3-x) -5^(2-2x)
) -
5^(x-3)
≥ 0 ;
(
30*5^(x+3) -5^(-x-1) -1 +5^(-x-1)
) /(
5^(3-x) -5^(2-2x)
)
≥ 0 ;
(
30*5^(x+3) -1
)
/
(
5^(3-x) -5^(2-2x)
)
≥ 0 ;
6*5⁴
(
5^x -1/6*5⁴
) /
5^(3-2x)* (5^x -1/5)
≥ 0⇔
(5^x -1/6*5⁴
)
/(5^x -1/5)
≥ 0.
x ∈(-∞;Loq_5 1/6*5⁴ ] U (-1 ;∞).
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Answers & Comments
Verified answer
( 30*5^(x+3) -0,2^(x+1) ) /( 5^(3-x) -25^(1-x)) ≥5^(x-3) ;( 30*5^(x+3) -5^(-x-1) ) /( 5^(3-x) -5^(2-2x)) ≥5^(x-3) ;
( 30*5^(x+3) -5^(-x-1) ) /( 5^(3-x) -5^(2-2x)) - 5^(x-3) ≥ 0 ;
( 30*5^(x+3) -5^(-x-1) -1 +5^(-x-1) ) /( 5^(3-x) -5^(2-2x)) ≥ 0 ;
( 30*5^(x+3) -1 ) / ( 5^(3-x) -5^(2-2x)) ≥ 0 ;
6*5⁴ ( 5^x -1/6*5⁴) / 5^(3-2x)* (5^x -1/5) ≥ 0⇔
(5^x -1/6*5⁴)/(5^x -1/5) ≥ 0.
x ∈(-∞;Loq_5 1/6*5⁴ ] U (-1 ;∞).