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Задания 129 и 130
(задания написано на фотографии)
Задания 129 и 130
(задания написано на фотографии)
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129.------
1) ( 0,1) ^ (- Lg 0,3 ) =(10⁻¹ )* ^ (- Lg 0,3 ) =(10)* ^ (Lg 0,3 ) = 0,3 .
2) 10 ^(-Lg4) = 10 ^(Lg4 ⁻¹ ) = 4 ⁻¹ = 1/4. || 0,25 ||
3) 5 ^( -Log 5 3) = 5 ^( Log 5 3 ⁻¹ ) = 3 ⁻¹ =1/3.
4) 1/ 6 ^(-Log 6 4) =( 6⁻¹)^ (-Log 6 4) =6^ (Log 6 4) ) =4.
130.
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1) 4Log(1/2) 3 -(2/3) Log (1/2) 27 -2 Log (1/2) 6 =
Log(1/2) 3⁴ - Log (1/2) (3³)^(2/3) - Log (1/2) 6² =
Log(1/2) 3⁴ - Log (1/2) 3² - Log (1/2) 6² = Log(1/2) 3⁴/(3²* 6²) =
Log(1/2) 3²/ 6² = Log(1/2) (3/ 6)² = Log(1/2) (1/ 2)² =2.
или по другому:
4Log(1/2) 3 -(2/3) Log (1/2) 27 -2 Log (1/2) 6 =
4Log(1/2) 3 - (2/3)Log( 1/2) 3³ -2 Log (1/2) 6 =
4Log(1/2) 3 - 2 Log (1/2) 3 - 2Log (1/2) 6 =2Log(1/2) 3 - 2 Log (1/2) 6=
2*(Log(1/2) 3 - Log (1/2) 6 ) =2 Log (1/2) (3/6 )=2 Log (1/2) (1/2 ) =2
Log(1/2) 3²/ 6² = Log(1/2) (3/ 6)² = Log(1/2) (1/ 2)² =2.
2) ( 2/3)*Lg0,001 +Lg ∛1000 -(3/5)*Lg √10000 =
( 2/3)*Lg10⁻³ +Lg ∛10³ -(3/5)*Lg √10⁴ = ( 2/3)*(-3) +Lg10 -(3/5)*Lg 10² =
(2/3)*(-3) +1 -(3/5)*2 = -2 +1 - 1,2 = - 2,2 .