מתמטיקה - 4 יח"ל - כיתה י"ב - חלק א'

ﺟﺑﺭ ﻭﻣﻘﺩّﻣﺔ ﻟﻠﺗّﺣﻠﻳﻝ ﺍﻟﺭّﻳﺎﺿﻲ ﻟﻠﺩّﻭﺍﻝ ﺍﻷﺳّﻳّﺔ ﻭﺍﻟﻠّﻭﻏﺭﻳﺛﻣﻳّﺔ

- 55 -

ﺍﻟﻔﺻﻝ :5 ﺍﻟﻠّﻭﻏﺭﻳﺛﻣﺎﺕ





0 .6

.

(3) ﺟﺪﻭﺍ ﻗﻴﻤﺔ x ، ﺍﻟّﺘﻲ ﺗﺤﻘّﻖ

x

2.3

e

اﻟﺤﻞّ:

0.6 x  

2.3 ln

2.3 0.8329 0.6 0.6      . ln x

ﺃﻱ ﺃﻥ

1.388







ﺗﻤ ﺎﺭﻳﻦ ﻟﻠﻌﻤﻞ ﺍﻟﺬّﺍﺗﻲ

ﺍِﻧﺘﺒﻬﻮﺍ : ﻟﻠﺘّﻤﺎﺭﻳﻦ (6) – (1) ﻟﻢ ﺗُﻌﻂ ﺃﺟﻮﺑﺔ ﻧﻬﺎﺋﻴّﺔ . ﻋﻠﻴﻜﻢ ﺍﻟ ﻔﺤﺺ ﻣﻊ ﺍﻟﻤﻌﻠّﻢ ﻓﻲ ﺍﻟﺼّﻒ . (1) ﺍِﻧﺘﻘﻠﻮﺍ ﻣﻦ ﻣﺘﺴﺎﻭﻳﺎﺕ ﺃﺳّﻴّﺔ ﺇﻟﻰ ﻣﺘﺴﺎﻭﻳﺎﺕ ﻟﻮﻏﺮﻳﺜﻤﻴّﺔ ) ﻣﺜﺎل: 3 2 8 3 2 8 log    :(

2  

4 2 16 

2 3 9 

1 1 00

)ﺝ(

)ﺏ(

)ﺃ(

10

1 .5   _ i 1 4

2 3 8 4 

1 2 25 5 

)ﻭ(

)ﻫـ(

)ﺩ(

8

8 1 log   

1 .5

1 2

:(

(2) ﺍِﻧﺘﻘﻠﻮﺍ ﻣﻦ ﻣﺘﺴﺎﻭﻳﺎﺕ ﻟﻮﻏﺮﻳﺜﻤﻴّﺔ ﺇﻟﻰ ﻣﺘﺴﺎﻭﻳﺎﺕ ﺃﺳّﻴّﺔ ) ﻣﺜﺎل :

4 8

4

32 2 log 

3 81 4 log  3 9 2 log 

8 64 2 log 

1 2

)ﺝ(

)ﺏ(

)ﺃ(

4



7 1 0 log 

1 1 0

)ﻭ(

)ﻫـ(

)ﺩ(

log

1

1 0

2 log  :(

(3) ﺍِﺣﺴﺒﻮﺍ ﺩﻭﻥ ﺍﺳﺘﺨﺪﺍﻡ ﺍﻵﻟﺔ ﺍﻟﺤﺎﺳﺒﺔ ﺍﻟﻠّﻮﻏﺮﻳﺜﻤﺎﺕ ﺍﻟﺘّﺎﻟﻴﺔ ﺣﺴﺐ ﺍﻷﺳﺎﺱ ) 2

) ﻳﻤﻜﻦ ﺍﻻﺳﺘﻌﺎﻧﺔ ﺑﻜﺘﺎﺑﺔ ﻣﻌﺎﺩﻟﺔ ﺃُﺳّﻴّﺔ ﻣﻼﺋﻤﺔ .( )ﺃ( 2 16 log )ﺏ( 2 1 4 log

)ﺝ(

log

2

2

4

)ﻫـ(

)ﺩ(

2 2 2 log ( )

log

8

2

5 log  :(

(4) ﺍِﺣﺴﺒﻮﺍ ﺩﻭﻥ ﺍﺳﺘﺨﺪﺍﻡ ﺍﻵﻟﺔ ﺍﻟﺤﺎﺳﺒﺔ ﺍﻟﻠّﻮﻏﺮﻳﺜﻤﺎﺕ ﺍﻟﺘّﺎﻟﻴﺔ ﺣﺴﺐ ﺍﻷﺳﺎﺱ ) 5

) ﻳﻤﻜﻦ ﺍﻻﺳﺘﻌﺎﻧﺔ ﺑﻜﺘﺎﺑﺔ ﻣﻌﺎﺩﻟﺔ ﺃُﺳّﻴّﺔ ﻣﻼﺋﻤﺔ .( )ﺃ( 5 5 log )ﺏ( 5 125 log

)ﺝ(

log

5

5

1

5 1 1 25 log

3

)ﻭ(

)ﻫـ(

)ﺩ(

log

log

5

5

5

5

(5) ﺍِﺣﺴﺒﻮﺍ ﺩﻭﻥ ﺍﺳﺘﺨﺪﺍﻡ ﺍﻵﻟﺔ ﺍﻟﺤﺎﺳﺒﺔ ﺍﻟﻠّﻮﻏﺮﻳﺜﻤﺎﺕ ﺍﻟﺘّﺎﻟﻴﺔ ﺣﺴﺐ ﺍﻷﺳﺎﺱ :10 )ﺃ( 10,000 log )ﺏ( 1 1 00 log )ﺝ( 10 log )ﺩ( 1 1 0 log )ﻫـ( 10 10 log ﻣﻼﺣﻈﺔ: ﺇﺫﺍ ﻟﻢ ﻳُﻜﺘَﺐ ﺃﺳﺎﺱ ﻟﻠﻮﻏﺮﻳﺜﻢ، ﻳﻜﻮﻥ ﺍﻷﺳﺎﺱ ﻫﻮ ﺍﻟﻌﺪﺩ . 10 ﻣﺜﺎل: ﻧﻜﺘﺐ

1 0 1,000 log ﻫﻜﺬﺍ : 1,000 log ، ﻭﻳﺘﺤﻘّﻖ : 1,000 3 log  .

© ﺟﻣﻳﻊ ﺍﻟﺣﻘﻭﻕ ﻣﺣﻔﻭﻅﺔ ﻟﺟﺎﺑﻲ ﻳﻛﻭﺋﻳﻝ –

– ﺭﻳﺎﺿﻳّﺎﺕ ﻟﻁﻼّﺏ 4 ﻭﺣﺩﺍﺕ ﺗﻌﻠﻳﻣﻳّﺔ – ﺍﻟﺻّﻑ ﺍﻟﺛّﺎﻧﻲ ﻋﺷﺭ – ﺍﻟﻣﻧﻬﺞ ﺍﻟﺟﺩﻳﺩ