Question

Помогите,пожалуйста, с логарифмами (По подробнее,если можно) 1)log3 8+3log3 9/2 2)log7 196- 2log7 2 3)log2 √3+1/2log2 4/3

Answer 1

1) log₃ 8 + 3log₃ (9/2) = log₃ 8 + log₃ (9/2)³ =
    = log₃ 2³ + log₃ (9³/2³) = log₃ ((2³ * 3⁶)/2³) = log₃ 3⁶ = 6

2) log₇ 196 - 2log₇ 2 = log₇ 196 - log₇ 2² = log₇ 196 - log₇ 4 =
    = log₇ (196/4) = log₇ 49 = log₇ 7² = 2

3) log₂ √3 + 1/2 log₂ (4/3) = log₂ √3 + log₂ (4/3)^(1/2) =
    = log₂ ((√3*√4)/√3) = log₂ √4 = log₂ 2 = 1