Question

Упростите выражения: log 9 121+2 log 9 (9\11);log 5 100 + 2 log 5 1\2 ;log 4 9+2log 4(4\3)

Answer 1

Log₉121 + 2log₉(9/11) = log₉11² + 2(log₉9 - log₉11) = 2log₉11 + 2(1 - log₉11) = 2log₉11 + 2 - 2log₉11 = 2
log₅100 + 2log₅(1/2) = log₅10² +2log₅2⁻¹ = 2log₅10 - 2log₅2 = 2(log₅10 - log₅2) = 2log₅(10/2) = 2 log₅5 = 2
log₄9 + log₄(4/3) = log₄3² + log₄4 - log₄3 = 2log₄3 + 1 - log₄3 = log₄3 + 1 = log₄3 + log₄4 = log₄12