Question

1.Вычислить: a) log1/2 2; б)log4 32; в) log2 * log2 16; г)log4 5+ log4 25 2.Упростить выражение а)log2 16+log2 8 -log2 2 б)log3 16- log3 48 +log3 27 3.Сравнить выражение а)log 2 128 и log2 32; б)lg 0.9 и lg (0,9)²; в)lg 48 - lg 9 и lg 21 - lg 4; г)log4 11+ log4 9 и log4 (11+9).

Answer 1

Ответ:

Пошаговое объяснение:

1) log1/2 2 = -log2 2= -1

2)log4 32 = 1/2log2 2^5=2.5

3)log2(?) * log2 16 =

a)log2 16+log2 8 -log2 2 = log2 2^4 + log2 2^3 + 1=4+3+1=8

б)log3 16- log3 48 +log3 27=log3 (16/48) + log3 3^3 = -log3 3 + 3= -1+3 = 2

log 2 128 > log2 32

lg 0.9 < lg (0,9)²

lg 48 - lg 9 > lg 21 - lg 4

log4 11+ log4 9 > log4 (11+9)

Answer 2

1. Решение: a) log1/2 2 = log2/log2(1/2) = log2/-log2(2) = log2(-1) = undefined

b) log4 32 = log2 32 / log2 4 = 5/2

c) log2 * log2 16 = log2(16^log2) = log2(2^4) = 4

г) log4 5+ log4 25 = log4(5*25) = log4(125) = 3

2. Решение: a) log2 16+log2 8 -log2 2 = log2(16*8/2) = log2(64) = 6

б) log3 16- log3 48 +log3 27 = log3(16/48*27) = log3(9/4) = 2 - log3(2)

3. Решение: a) log2 128 = log2(2^7) = 7, log2 32 = log2(2^5) = 5, 7 > 5, log2 128 > log2 32

б) lg 0.9 = -0.04575749056, lg (0,9)² = lg 0.81 = -0.09151410169, -0.04575749056 < -0.09151410169, lg 0.9 > lg (0,9)²

в) lg 48 - lg 9 = lg (48/9) = lg 5/3, lg 21 - lg 4 = lg (21/4), lg 5/3 > lg 21/4

г) log4 11+ log4 9 = log4(11*9) = log4(99), log4 (11+9) = log4(20), log4(99) > log4(20)