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ЛОГАРИФМИЧЕСКИЕ УРАВНЕНИЯ

ЛОГАРИФМИЧЕСКИЕ УРАВНЕНИЯ. ( лекция). log a x = b. x > 0 a > 0 a ≠ 1. НАЗОВИТЕ НОМЕРА ЛОГАРИФМИЧЕСКИХ УРАВНЕНИЙ, ИМЕЮЩИХ СМЫСЛ. 1.log 2 x = -3 2. log 1 x = log 1 5 3. log -1 2 x = 5 4. log 2 2 x + log 2 x = 0 5. log 16 x + log 4 x = log 8 x.

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ЛОГАРИФМИЧЕСКИЕ УРАВНЕНИЯ

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  1. ЛОГАРИФМИЧЕСКИЕ УРАВНЕНИЯ ( лекция)

  2. logax = b x > 0 a > 0 a ≠ 1

  3. НАЗОВИТЕ НОМЕРА ЛОГАРИФМИЧЕСКИХ УРАВНЕНИЙ, ИМЕЮЩИХ СМЫСЛ 1.log2x = -3 2. log1x = log15 3. log-12x = 5 4. log22x + log2x = 0 5. log16x + log4x = log8x

  4. 1 метод: решение уравнений, основанное на определении логарифма. logax = b x = ab НАПРИМЕР: log5(x – 2) = 1

  5. РЕШИТЕ УРАВНЕНИЯ • lg(x + 3) = 2lg2 + lgx • lg(lgx) = 0 • log7x + logx7 = 2,5 • xlgx + 2 = 100x • logx2 - logx5 + 1,25 = 0 • Log42x – log4x – 2 = 0 • Log3(2x + 1) = 2 • Logx-6(x2 – 5) = logx-6(2x + 19) • xlog x = 16 • Log2(3x – 6) = log2(2x – 3) • Logx+1(2x2+1) = 2 • X1+log x = 9

  6. 2 метод: потенцирование logaf(x) = logag(x) f(x) = g(x) f(x) > 0, g(x) >0, a > 0, a ≠ 1 НАПРИМЕР: log5x = log5(6 – x2)

  7. РЕШИТЕ УРАВНЕНИЯ • lg(x + 3) = 2lg2 + lgx • lg(lgx) = 0 • log7x + logx7 = 2,5 • xlgx + 2 = 100x • logx2 - logx5 + 1,25 = 0 • Log42x – log4x – 2 = 0 • Log3(2x + 1) = 2 • Logx-6(x2 – 5) = logx-6(2x + 19) • xlog x = 16 • Log2(3x – 6) = log2(2x – 3) • Logx+1(2x2+1) = 2 • X1+log x = 9

  8. 3 метод: приведение логарифмического уравнения к квадратному Aloga2f(x) + Blogaf(x) + C = 0 A ≠ 0, f(x) > 0, a > 0, a ≠ 0 способ решения: подстановка y = logaf(x) тогда уравнение примет вид: Ау2 + Ву + С = 0. НАПРИМЕР: log32x – log3x = 2

  9. РЕШИТЕ УРАВНЕНИЯ • lg(x + 3) = 2lg2 + lgx • lg(lgx) = 0 • log7x + logx7 = 2,5 • xlgx + 2 = 100x • logx2 - logx5 + 1,25 = 0 • Log42x – log4x – 2 = 0 • Log3(2x + 1) = 2 • Logx-6(x2 – 5) = logx-6(2x + 19) • xlog x = 16 • Log2(3x – 6) = log2(2x – 3) • Logx+1(2x2+1) = 2 • X1+log x = 9

  10. 4 метод: логарифмирование обеих частей уравнения. НАПРИМЕР: xlog x = 81

  11. РЕШИТЕ УРАВНЕНИЯ • lg(x + 3) = 2lg2 + lgx • lg(lgx) = 0 • log7x + logx7 = 2,5 • xlgx + 2 = 100x • logx2 - logx5 + 1,25 = 0 • Log42x – log4x – 2 = 0 • Log3(2x + 1) = 2 • Logx-6(x2 – 5) = logx-6(2x + 19) • xlog x = 16 • Log2(3x – 6) = log2(2x – 3) • Logx+1(2x2+1) = 2 • X1+log x = 9

  12. 5 метод: приведения логарифмов к одному основанию Используют формулы: logab = logab = loga b = logab НАПРИМЕР: log16x + log4x + log2x = 7

  13. РЕШИТЕ УРАВНЕНИЯ • lg(x + 3) = 2lg2 + lgx • lg(lgx) = 0 • log7x + logx7 = 2,5 • xlgx + 2 = 100x • logx2 - logx5 + 1,25 = 0 • Log42x – log4x – 2 = 0 • Log3(2x + 1) = 2 • Logx-6(x2 – 5) = logx-6(2x + 19) • xlog x = 16 • Log2(3x – 6) = log2(2x – 3) • Logx+1(2x2+1) = 2 • X1+log x = 9

  14. ЛОГАРИФМИЧЕСКИЕУРАВНЕНИЯ

  15. СПАСИБО ЗАУРОК

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