diketahui sistem persamaan 2log x + 2log y^3 =13 dan 2log x - 2log y = 15 nilai x+y adalah

2Log x + 2Log y³ = 13
2(Log x + Log y³) = 13
Log x + Log y³ = 13/2

2Log x - 2Log y = 15
2(Log x - Log y) = 15
Log x - Log y = 15/2
Log x = 15/2 + Log y

Samakanan...
Log x = Log x
13/2 - Log y³ = 15/2 + Log y
3Log y + Log y = 13/2 - 15/2
4Log y = -1
Log y = -1/4
10^(-1/4) = y

Log x = 15/2 + Log y
Log x = 15/2 - 1/4
Log x = 29/4
10^(29/4) = x

Maka...
x + y
= 10^(-1/4) + 10^(29/4)
= ⁴√[1/10] + ⁴√[10^29]

Bab Logaritma
Matematika SMA Kelas X

²log x + ²log y³ = 13
²log (x y³) = 13
xy³ = 2¹³

²log x - ²log y = 15
²log (x/y) = 15
x/y = 2¹⁵
x = 2¹⁵ . y

xy³ = 2¹³
y . 2¹⁵ . y³ = 2¹³
y¹⁺³ = 2¹³ : 2¹⁵
y⁴ = 2¹³⁻¹⁵
y = (2⁻²)^(1/4)
y = 2^(-2/4)
y = 2^(-1/2)
y = 1/√2
y = (1/2) √2

x = 2¹⁵ . y
x = 2¹⁵ . 2^(-1/2)
x = 2^(15 - 1/2)
x = 2^(14 1/2)
x = 2^(29/2)

x + y = 2^(29/2) + 2^(-1/2)
x + y = 16.384 √2 + (1/2) √2
x + y = 16.384 1/2 √2