Question

OBLICZ :

1 ) log₆8+log₆27 =

2 ) log₄+log25=

3 ) log³₂27+log³₂ ⅛ =

4 ) log₂48-log₂3 =

5 ) log₀,₂250-log₀,₂2=

6 ) log√₃18-log√₃2=

7 )log₁₂4+log₁₂36=

8 ) log⅖40+log⅖ 1/100=

9 ) log₄40+log₄1/5=

10) log₅3-log₅15=

11)log4/9 8-log 4/9 27=

DAJE NAJJ!

Answer 1

1 ) log₆8+log₆27 = log₆ (8 * 27) = log₆ 216 = log₆ 6³ = 3 log₆ 6 = 3 * 1 = 3

 

2 ) log₄+log25=  brakuje danych

3 ) log³₂27+log³₂ ⅛ = coś tu namieszane jest

 

4 ) log₂48-log₂3 = log₂ (48/3) = log₂ 16 = log₂ 2⁴ = 4 *log₂ 2 = 4 * 1 = 4

 

5 ) log₀,₂250-log₀,₂2= log₀,₂ (250/2) = log₀,₂ 125 = log₀,₂ 5³ = log₀,₂ (1/5)^(-3) = -3 *log₀,₂ (1/5) = -3 * 1 = -3

 

6 ) log√₃18-log√₃2= log√₃ (18 : 2) = log√₃  9 = log√₃ (√3)⁴ = 4 * log√₃ (√3) = 4 * 1 = 4

 

7 )log₁₂4+log₁₂36= log₁₂ (4 * 36) = log₁₂ 144 = log₁₂ 12² = 2 * log₁₂ 12 = 2 * 1 = 2

 

8 ) log⅖40+log⅖ 1/100= log2/5 (40 * 1/100) = log2/5 (2/5) = 1

 

9 ) log₄40+log₄1/5= log₄ (40 * 1/5) = log₄ 8 = log₄ 2^3 = 3 * log₄ 2 = 3 * log₄ 4^(1/2) = 3 * 1/2 = 3/2 = 1,5

 

10) log₅3-log₅15= log₅ (3 : 15) = log₅ 1/5 = log₅ 5^(-1) = -1 * log₅ 5 = -1

 

11)log4/9 8-log 4/9 27= log4/9 (8 : 27) = log4/9 8/27 = log4/9  (2/3)³ = 3 * log4/9 2/3 = 3 * log4/9 (4/9)^(1/2) = 3 * 1/2 = 3/2 = 1,5