12. log₀,₅5⋅log₅1.25

log₀,₅5⋅log₅1.25 = log₀.₅5 ⋅ log₅(5/4) = log(1/2)5 ⋅ log₅(5/4) = - log₂5 ⋅ log₅(5/4) = - log₂5 ⋅ (log₅5 - log₅4) = - log₂5 ⋅ (1 - log₅4) = -log₂5 ⋅ (1 - log₅2²) = -log₂5 ⋅ (1 - 2log₅2) = -log₂5 + log₂5 ⋅ 2log₅2 = -log₂5 + 2log₂5 ⋅ log₅2 = -log₂5 + 2log₂5 ⋅ 1/log₂5 = -log₂5 + 2 = 2 - log₂5

Ответ: 2-log₂5