Bài 1: a) 3^x+2 – 5.3^x = 36 b) 7.4^x-1 + 4^x+1 = 23 2.2^2x + 4^3.4^x = 1056

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1. `a, 3^(x+2) – 5.3^x = 36`

   `3^x.(3^2- 5 ) = 36`

   `3^x . 4 = 36`

   `3^x= 36 : 4`

   `3^x= 9`

   `3^x=3^2`

   `=> x = 2`

   ` b, 7.4^x-1 + 4^x+1 = 23`

   `4^(x-1). ( 7+4^2 ) = 23`

   `4^(x-1).( 7 + 16 ) = 23`

   `4^(x-1). 23 = 23`

   `4^(x-1) = 23 : 23`

   `4^(x-1)= 1`

   `4^(x-1)= 4^0`

   `→ x – 1 = 0`

   `→ x = 0 + 1`

   `→ x = 1`

   `c,2.2^2x + 4^3.4^x = 1056`

   `2^(2x+1)+2^6.2^(2x)=1056`

   `2^(2x).(2+2^6)=1056`

   `2^(2x).( 2 + 64 ) = 1056

   `2^(2x). 66 = 1056`

   `2^(2x)= 1056 : 66`

   `2^(2x)= 16`

   `2^(2x)=2^4`

   `→ 2x = 4`

   `→ x = 4 : 2`

   `→ x = 2`

    

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2. Đáp án: a ) x = 2 ; b ) x = 1 ; c ) x = 2

    

   Giải thích các bước giải:

    a ) $3^{x+2}$ – 5 . $3^{x}$ = 36

   $3^{x}$ . ( $3^{2}$ – 5 ) = 36

   $3^{x}$ . 4 = 36

   $3^{x}$ = 36 : 4

   $3^{x}$ = 9

   $3^{x}$ = $3^{2}$

   → x = 2

   b ) 7 . $4^{x-1}$ + $4^{x+1}$ = 23

   $4^{x-1}$ . ( 7 + $4^{2}$ ) = 23

   $4^{x-1}$ . ( 7 + 16 ) = 23

   $4^{x-1}$ . 23 = 23

   $4^{x-1}$ = 23 : 23

   $4^{x-1}$ = 1

   $4^{x-1}$ = $4^{0}$

   → x – 1 = 0

   → x = 0 + 1

   → x = 1

   c ) 2 . $2^{2x}$ + $4^{3}$ . $4^{x}$ = 1056

   $2^{2x+1}$ + $2^{6}$ . $2^{2x}$ = 1056

   $2^{2x}$ . ( 2 + $2^{6}$ ) = 1056

   $2^{2x}$ . ( 2 + 64 ) = 1056

   $2^{2x}$ . 66 = 1056

   $2^{2x}$ = 1056 : 66

   $2^{2x}$ = 16

   $2^{2x}$ = $2^{4}$

   → 2x = 4

   → x = 4 : 2

   → x = 2

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