Tarkib

• Qadamlar
• 4 -usul 1: Birinchidan, eksponensial shaklda logarifmik ifodani ifodalashni o'rganing.
• 4 -usul 2: "x" ni hisoblang
• 4 -usulning 3 -usuli: "x" ni mahsulot logarifmasining formulasi orqali hisoblang
• 4 -usul 4: "x" ni bo'linma logarifmasi formulasi orqali hisoblang

Bir qarashda, logarifmik tenglamalarni yechish juda qiyin, lekin agar siz logarifmik tenglamalarni eksponensial tenglamalarni yozishning yana bir usuli ekanligini tushunsangiz, bunday bo'lmaydi. Logarifmik tenglamani echish uchun uni eksponensial tenglama sifatida ifodalang.

Qadamlar

4 -usul 1: Birinchidan, eksponensial shaklda logarifmik ifodani ifodalashni o'rganing.

1. 1 Logarifm ta'rifi. Logarifm raqamni olish uchun bazani ko'tarish kerak bo'lgan ko'rsatkich sifatida aniqlanadi. Quyida keltirilgan logarifmik va eksponensial tenglamalar ekvivalentdir.
   • y = log_b (x)
     • Shu shart bilan: b = x
   • b logarifmaning asosi hisoblanadi va
     • b> 0
     • b ≠ 1
   • NS logarifmaning argumentidir va da - logarifm qiymati.
2. 2 Bu tenglamaga qarang va logarifmaning asosini (b), argumentini (x) va qiymatini (y) aniqlang.
   • Misol: 5 = jurnal₄(1024)
     • b = 4
     • y = 5
     • x = 1024
3. 3 Tenglamaning bir tomoniga (x) logarifmining argumentini yozing.
   • Misol: 1024 =?
4. 4 Tenglamaning boshqa tomoniga, (y) logarifm darajasiga ko'tarilgan asosni (b) yozing.
   • Misol: 4 * 4 * 4 * 4 * 4 = ?
     • Bu tenglamani quyidagicha ifodalash mumkin: 4
5. 5 Endi logarifmik ifodani eksponensial ifoda sifatida yozing. Tenglamaning ikkala tomoni teng ekanligiga ishonch hosil qilib, javobning to'g'riligini tekshiring.
   • Misol: 4 = 1024

4 -usul 2: "x" ni hisoblang

1. 1 Logarifmni tenglamaning bir tomoniga o'tkazib ajratib oling.
   • Misol: jurnali₃(x + 5) + 6 = 10
     • jurnali₃(x + 5) = 10 - 6
     • jurnali₃(x + 5) = 4
2. 2 Tenglamani eksponent sifatida qayta yozing (buning uchun oldingi bo'limda tasvirlangan usuldan foydalaning).
   • Misol: jurnali₃(x + 5) = 4
     • Logarifm ta'rifiga ko'ra (y = log_b (x)): y = 4; b = 3; x = x + 5
     • Ushbu logarifmik tenglamani eksponent sifatida qayta yozing (b = x):
     • 3 = x + 5
3. 3 "X" ni toping. Buning uchun ko’rsatkichli tenglamani yeching.
   • Misol: 3 = x + 5
     • 3 * 3 * 3 * 3 = x + 5
     • 81 = x + 5
     • 81 - 5 = x
     • 76 = x
4. 4 Oxirgi javobingizni yozing (avval tekshiring).
   • Misol: x = 76

4 -usulning 3 -usuli: "x" ni mahsulot logarifmasining formulasi orqali hisoblang

1. 1 Mahsulot logarifmasi uchun formulalar: ikkita dalilning mahsulotining logarifmasi ushbu argumentlarning logarifmlari yig'indisiga teng:
   • jurnali_b(m * n) = jurnal_b(m) + jurnal_b(n)
   • bu erda:
     • m> 0
     • n> 0
2. 2 Logarifmni tenglamaning bir tomoniga o'tkazib ajratib oling.
   • Misol: jurnali₄(x + 6) = 2 - jurnal₄(x)
     • jurnali₄(x + 6) + jurnal₄(x) = 2 - jurnal₄(x) + jurnal₄(x)
     • jurnali₄(x + 6) + jurnal₄(x) = 2
3. 3 Agar tenglamada ikkita logarifm yig'indisi bo'lsa, mahsulotning logarifmasi formulasini qo'llang.
   • Misol: jurnali₄(x + 6) + jurnal₄(x) = 2
     • jurnali₄[(x + 6) * x] = 2
     • jurnali₄(x + 6x) = 2
4. 4 Tenglamani eksponensial shaklda qayta yozing (buning uchun birinchi bo'limda ko'rsatilgan usuldan foydalaning).
   • Misol: jurnali₄(x + 6x) = 2
     • Logarifm ta'rifiga ko'ra (y = log_b (x)): y = 2; b = 4; x = x + 6x
     • Ushbu logarifmik tenglamani eksponent sifatida qayta yozing (b = x):
     • 4 = x + 6x
5. 5 "X" ni toping. Buning uchun ko’rsatkichli tenglamani yeching.
   • Misol: 4 = x + 6x
     • 4 * 4 = x + 6x
     • 16 = x + 6x
     • 16 - 16 = x + 6x - 16
     • 0 = x + 6x - 16
     • 0 = (x - 2) * (x + 8)
     • x = 2; x = -8
6. 6 Oxirgi javobingizni yozing (avval tekshiring).
   • Misol: x = 2
   • E'tibor bering, "x" qiymati manfiy bo'lishi mumkin emas, shuning uchun yechim x = - 8 e'tiborsiz qoldirilishi mumkin.

4 -usul 4: "x" ni bo'linma logarifmasi formulasi orqali hisoblang

1. 1 Qismning logarifmasi uchun formulalar: ikkita argumentning bo'lagi logarifmasi bu argumentlarning logarifmlari orasidagi farqga teng:
   • jurnali_b(m / n) = jurnal_b(m) - jurnal_b(n)
   • bu erda:
     • m> 0
     • n> 0
2. 2 Logarifmni tenglamaning bir tomoniga o'tkazib ajratib oling.
   • Misol: jurnali₃(x + 6) = 2 + log₃(x - 2)
     • jurnali₃(x + 6) - jurnal₃(x - 2) = 2 + log₃(x - 2) - jurnal₃(x - 2)
     • jurnali₃(x + 6) - jurnal₃(x - 2) = 2
3. 3 Agar tenglamada ikkita logarifmaning farqi bo'lsa, bo'lakning logarifmasi formulasini qo'llang.
   • Misol: jurnali₃(x + 6) - jurnal₃(x - 2) = 2
     • jurnali₃[(x + 6) / (x - 2)] = 2
4. 4 Tenglamani eksponensial shaklda qayta yozing (buning uchun birinchi bo'limda ko'rsatilgan usuldan foydalaning).
   • Misol: jurnali₃[(x + 6) / (x - 2)] = 2
     • Logarifm ta'rifiga ko'ra (y = log_b (x)): y = 2; b = 3; x = (x + 6) / (x - 2)
     • Ushbu logarifmik tenglamani eksponent sifatida qayta yozing (b = x):
     • 3 = (x + 6) / (x - 2)
5. 5 "X" ni toping. Buning uchun ko’rsatkichli tenglamani yeching.
   • Misol: 3 = (x + 6) / (x - 2)
     • 3 * 3 = (x + 6) / (x - 2)
     • 9 = (x + 6) / (x - 2)
     • 9 * (x - 2) = [(x + 6) / (x - 2)] * (x - 2)
     • 9x - 18 = x + 6
     • 9x - x = 6 + 18
     • 8x = 24
     • 8x / 8 = 24/8
     • x = 3
6. 6 Oxirgi javobingizni yozing (avval tekshiring).
   • Misol: x = 3