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[tex]log_{\sqrt{ab} } (ab^{2} ) \\log_{a} b=3[/tex]

Ответ задания на картинке:

log (√ab) ab² = log(√ab) ab*b = 2 (log(ab) ab + log (ab) b) = 2*(1 + 1/log(b) ab) = 2 * (1 + 1/(log(b) a + log(b) b) = 2*(1 + 1/(1/log(a) b + 1)

log(a) b = 3

2*(1 + 1/(1/3 + 1)) = 2*(1 + 3/4) = 2*7/4 = 7/2 = 3,5

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log(a) bc = log(a) b + log(a) c

log (a^k) b = 1/k * log(a) b

log(a) b = 1/log(b) a