Показательное неравенство[tex] \frac{30* 5^{x+3} - 0,2^{x+1} }{ 5^{3-x}- 25^{1-x} } \geq 5^{x-3} [/tex]. Created by opgqwav8w1m. algebra-ru

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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

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( 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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pomogite reshit trigonometricheskoe uravnenie02b77d4b454211c5eca135f037e9a04b 82064

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