1,tìm x 2.3 mũ x=162 2 mũ x – 15=17 (7 mũx -11)mũ 3 = 5 mũ 2+200 x mũ 10=x

0 bình luận về “1,tìm x 2.3 mũ x=162 2 mũ x – 15=17 (7 mũx -11)mũ 3 = 5 mũ 2+200 x mũ 10=x”

1. a) 3^x=162

   2.3∧X=2.3∧4

   ⇒x=4

   b)2∧x -15=17

    2∧x=32

   2∧X=2∧5

   ⇒x=5

   (7x-11)∧3=5∧2+200

   (7x-11)∧3=25.32+200

   (7x-11)∧3=1000

   (7x-11)∧3=10∧3

   7x-11=10

   7x=21

   x=3

   x∧10=x 

   ⇒x∧10-x=0

   ⇒x.(x∧9-1)=0

   TH1:⇒x=0

   TH2:⇒x∧9-1=0⇒x=1

   Vậy x=0 hoặc x=1

    

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2. Giải thích các bước giải:

   `2.3 ^ x=162`
   `=>3^x=162:2`
   `=>3^x=81`
   `=>3^x=3^4`
   `=>x=4`
   `2 ^ x – 15=17`
   `=>2^x=17+15`
   `=>2^x=32`
   `=>2^x=2^5`
   `=>x=5`
   `(7.x-11)^3=5^2. 2^5+200`
   `=>(7.x – 11)^3=25 . 32+200`
   `=>(7.x – 11)^3=800+200`
   `=>(7.x – 11)^3=1000`
   `=>(7.x – 11)^3=10^3`
   `=>7.x – 11=10`
   `=>7.x = 10+11`
   `=>7.x=21`
   `=>x=21:7`
   `=>x=3`

   `x^10=x`
   `=>x^10-x=0`
   `=>x^9 . x-x.1=0`
   `=>x.(x^9 -1)=0`
   `=>`\(\left[ \begin{array}{l}x=0\\x^9 – 1=0\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=0\\x^9=0+1\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=0\\x^9=1\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=0\\x^9=1^9\end{array} \right.\) 
   `=>`\(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\) 

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