Question

Логарифмы, 2 задание, 4 пример

Answer 1

log(a^k) b^n = n/k * log(a) b

a^log(a) b = b

lg = log(10)

a^m/a^n = a^(m-n)

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log(5) 1/125 = log(5) 1/5^3 =  log(5) 5^-3 = -3

log(1/2) 1/8 = log(1/2) (1/2)^3 = 3

lg 100 = lg 10^2 = 2

lg 0.001 = lg 1/1000 = lg 1/10^3 = lg 10^-3 = -3

4^(1/2 - log(2) √3) = 2^2(1/2 - log(2) √3) = 2^(1 - 2log(2) √3) = 2/2^log(2) (√3)² = 2/3

(или 2^(1 - 2log(2)√3) = 2^(log(2) 2 - log(2) √3²) = 2^log(2) 2/3 = 2/3)