3 ^ ( ( x - 5 )/2 ) ≥ 3√ 3
3 ^ (( x - 5 )/2 ) ≥ 3 ^ 3/2
( x - 5 ) / 2 ≥ 3 / 2
x - 5 ≥ 3
x ≥ 8
Ответ [ 8 ; + ∞ )
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( 5/2 ) ^ ( 2x - 3 ) < 15 5/8
( 5/2 ) ^ ( 2x - 3 ) < 125/8
( 5/2 ) ^ ( 2x - 3 ) < ( 5/2 ) ^ 3
2x - 3 < 3
2x < 6
x < 3
Ответ ( - ∞ ; 3 )
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( 2/3 ) ^ ( x^2 + 5x ) > 1
( 2/3 ) ^ ( x ^2 + 5x ) < ( 2/3 ) ^ 0
x^2 + 5x < 0
x( x + 5 ) < 0
x < 0
x < - 5
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( 0,2 ) ^ ( 2x - 3 )( x - 2 ) < 5
5 ^ ( - ( 2x - 3 )( x - 2 )) > 5 ^ 0
( - 2x + 3 )( x - 2 ) > 0
- 2x^2 + 4x + 3x - 6 > 0
- 2x^2 + 7x - 6 > 0
D = 49 - 48 = 1
x1 = ( - 7 + 1 ) : ( - 4 ) = 1,5
x2 = ( - 7 - 1 ) : ( - 4 ) = 2