jika 2log a + 2log b = 12 dan 3 2log a - 2log b = 4. maka a+b

Misal x = 2log a dan y = 2log b
2log a + 2log b = 12 ==> x + y = 12
3 . 2log a - 2log b = 4 => 3x - y = 4
-------------------------------------------------- +
................................................ 4x = 16 => x = 4
x + y = 12 => 4 + y = 12 => y = 8
x = 4
=> 2log a = 2log 2^4
=> a = 2^4 = 16

y = 8
=> 2log b = 2log 2^8
=> b = 2^8 = 256

a + b = 16 + 256 = 272

Bab Logaritma
Matematika SMA Kelas X

²log a + ²log b = 12
²log ab = 12
ab = 2¹²

3 . ²log a - ²log b = 4
²log (a³ / b )_ = 4
a³ / b = 2⁴
b = a³/2⁴

a . b = 2¹²
a . a³/2⁴ = 2¹²
a¹⁺³ = 2¹² ⁺ ⁴
a⁴ = 2¹⁶
a = 2^(16 : 4)
a = 2⁴
a = 16

b = a³/2⁴
b = 2³ˣ⁴ . 2⁻⁴
b = 2¹² ⁻ ⁴
b = 2⁸
b = 256

a + b = 16 + 256 = 272