^4log(x^2-8x-7)=^5log(x^2-8x-7)

Logaritma

⁴log (x²-8x-7) = ⁵log (x²-8x-7)

Pembahasan

Karena numerus persamaan logaritma tersebut sama, maka:

x² – 8x – 7 = 1

x² – 8x – 8 = 0

a = 1, b = -8, dan c = -8

x₁,₂ = -b +- √b² – 4ac / 2a

x₁,₂ = -(-8) +- √(-8)² – 4(1)(-8) / 2(1)

x₁,₂ = 8 +- √64+32 / 2

x₁,₂ = 8 +- √96 / 2

x₁,₂ = 8 +- 4√6 / 2

x₁ = 8 + 4√6 / 2

x₁ = 4 + 2√6

x₂ = 8 – 4√6 / 2

x₂ = 4 – 2√6

Himpunan penyelesaian ialah x = 4+2√6 dan x = 4–2√6