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JohnS0apMacTavish
@JohnS0apMacTavish
July 2022
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Уравнение помогите))
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Санечка69
Verified answer
Log₅2³ + (2 - x)log₅5 = log₅(3ˣ - 5²⁻ˣ)
log₅8 + log₅(5²⁻ˣ) =
log₅(3ˣ - 5²⁻ˣ)
log
₅(8 · 5²⁻ˣ) =
log₅(3ˣ - 5²⁻ˣ)
8 · 5²⁻ˣ =
3ˣ - 5²⁻ˣ
8 · 5²⁻ˣ + 5²⁻ˣ = 3ˣ
9 · 5²⁻ˣ = 3ˣ
3² · 5²⁻ˣ = 3ˣ
5²⁻ˣ · 3²⁻ˣ = 1
15²⁻ˣ = 15⁰
2 - x = 0
x = 2
ОДЗ:
3ˣ - 5²⁻ˣ > 0
3ˣ > 5²⁻ˣ
3ˣ > 5² · 5
⁻ˣ
3ˣ ·
5ˣ > 25
15ˣ > 25
15ˣ > 15^(log₁₅25)
x > log₁₅ 25 > 1
Или:
Проверка: log₅2³ + 0 = log₅(3² - 5⁰)
log₅2³ =
log₅(9 - 1)
log₅8 =
log₅8 - верно
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Answers & Comments
Verified answer
Log₅2³ + (2 - x)log₅5 = log₅(3ˣ - 5²⁻ˣ)log₅8 + log₅(5²⁻ˣ) = log₅(3ˣ - 5²⁻ˣ)
log₅(8 · 5²⁻ˣ) = log₅(3ˣ - 5²⁻ˣ)
8 · 5²⁻ˣ = 3ˣ - 5²⁻ˣ
8 · 5²⁻ˣ + 5²⁻ˣ = 3ˣ
9 · 5²⁻ˣ = 3ˣ
3² · 5²⁻ˣ = 3ˣ
5²⁻ˣ · 3²⁻ˣ = 1
15²⁻ˣ = 15⁰
2 - x = 0
x = 2
ОДЗ: 3ˣ - 5²⁻ˣ > 0
3ˣ > 5²⁻ˣ
3ˣ > 5² · 5⁻ˣ
3ˣ · 5ˣ > 25
15ˣ > 25
15ˣ > 15^(log₁₅25)
x > log₁₅ 25 > 1
Или:
Проверка: log₅2³ + 0 = log₅(3² - 5⁰)
log₅2³ = log₅(9 - 1)
log₅8 = log₅8 - верно