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

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