Question

Determinati valoarea numarului natural x, stiind ca 9^x+2 +9^x+1 +9^x =71
·3^28 dau coroniță

Answer 1

$3*9^x+3=71+3^28$

3*(3²)^x+3=71*3^28

3*3^2x+1+3=71*3^28

3^2x+1+3=71*3^28

3^2x+1=71*3^28-3

2x+1=log₃(71*3^28-3)

2x=log₃(71*3^28-3)-1

x=log₃(71*3^28-3)/2-1/2

x=log₃(71*3^28-3)-1/2

x=15,44003 - asta daca vrei sub forma zecimala!



9^x+2 +9^x+1 +9^x =91 × 3^28
9^x×( 9^2 + 9^1 + 1 ) = 91 × 3^28
9^x × (81 + 9 + 1) = 91 × 3 ^28
9^x × 91 = 91 × 3^28
9^x = 91 × 3^28 : 91
9^x = 3^28
3^2x = 3^28
2x = 28
x = 28/2
x = 14 

Answer 2

9^x+2 +9^x+1 +9^x =91 × 3^28

9^x×( 9^2 + 9^1 + 1 ) = 91 × 3^28

9^x × (81 + 9 + 1) = 91 × 3 ^28

9^x × 91 = 91 × 3^28

9^x = 91 × 3^28 : 91

9^x = 3^28

3^2x = 3^28

2x = 28

x = 28 : 2

x = 14 (numar natural)