Question

Решите выражение

((-2log5 15)^2-(log5 9)^2+3*log5 15* log5 9)/log5 9-log5 15

Answer 1

(-2log²5 15 - log²5 9 + 3*log5 15* log5 9)/(log5 9-log5 15) =

(-(log²5 15  - 2*log5 15* log5 9 + log²5 9) + log5 15* log5 9 - log²5 15 )/(log5 9-log5 15) =

(-(log5 9  - log5 15)² + log5 15 (log5 9 - log5 15) )/(log5 9-log5 15) =

(log5 9  - log5 15)( log5 15 - (log5 9 - log5 15) )/(log5 9-log5 15) =

log5 15 - log5 9 + log5 15 = log5 (15*15)/9 = log5 (5²3²)/9 = log5 5² = 2