Преобразуйте логарифмическое выражение

log3 18/ log3 20= (log3 9 + log3 2) / (log3 4 + log3 5)=

(2 +a) /(2 a +log3 5)= (2 +a) /(2 a +1/ log5 3) = (2 +a) /(2 a +1/b)=

(2 +a)*b/( 2ab +1)- получилось у меня)

log 3(2)=a, log 5(3)=b
log 20(18) = log 3(18) / log 3(20) =
= log 3(2*3²) / log 3(5*2²) =
= (2+ log 3(2)) / (log 3(5) +2log 3(2)) =
= (2 + a) / (1/b + 2a) =
= b(a + 2) / (2ab + 1)
Ваш ответ:
(1+(a/2))/(2+(a/b) =
= [(2 + а) /а ] / [ (2b + a)/b ] =
= b(a + 2) / (2ab + a²)
????

125) log(mn) (m\Vn) = ----> (V- это корень квадратный)
= log(mn) m - log(mn) Vn = =>
__ log(mn) m = 1 \ log(m) mn = 1 \ (log(m) m + log(m) n) = 1 \ (1 + log(m) n)
__ log(mn) Vn = log(mn) n^(1\2) = 1\2 * log(mn) n = 1\2 * 1\log(n) mn =
= 1\2 * 1\(log(n) m + log(n) n) = 1\2 * 1\(log(n) m + 1)
=>
= 1\(1 + log(m) n) - 1\2 * 1\(log(n) m + 1) =
= 1\(1 + 2) - 1\2 * 1\(1\log(m) n + 1) =
= 1\3 - 1\2 * 1\(1\2 + 1) =
= 1\3 - 1\2 * 2\3 = 1\3 - 1\3 = 0