1.
а) log₂ (1/⁶√128) = log₂ (1/⁶√2⁷) = log₂ 2^(-⁷/₆)= -⁷/₆ = -1 ¹/₆
б) log₁₀ 8 + log₁₀ 125 = log₁₀ (8*125) =
log₂ 15 - log₂ (15/16) log₂ 15 -(log₂ 15 - log₂ 16)
= log₁₀ 1000 = log₁₀ 10³ = 3/4 =0.75
log₂ 15 -log₂ 15 +log₂ 16 log₂ 2⁴
в) 16^(1+log₄ 5) + 49^(log₇ 2) + log₂ 1 =
=16 * 16^(log₄ 5) + 7^(2log₇ 2) +0 =
= 16 * 4^(2log₄ 5) + 7^(log₇ 2²) =
= 16 * 4^(log₄ 5²) + 4 =
= 16*25+4=404
2.
a) log₅ (6x+2)=3
ОДЗ: 6x+2>0
6x> -2
x> -2/6
x> -1/3
6x+2 = 5³
6x+2=125
6x=125-2
6x=123
x=123/6
x= 20.5
Ответ: 20,5
б) log₄ x = log₄ 81+log₁₆ 5
ОДЗ: х>0
log₄ x = log₄ 81 +log₄² 5
log₄ x= log₄ 81 + log₄ 5^(¹/₂)
log₄ x= log₄ (81√5)
x=81√5
Ответ: 81√5