Question

Oblicz:

log ¹/₉ 27 = a
log a 2 = - ⅓
log₂₇ 81 = x
log 0,00001
log₁₆128
log (10⁻⁴)¹²

Answer 1

Log ¹/₉ 27 = a
(¹/₉)^a = 27
(1 / 3²)^a = 3³
(3⁻²)^a = 3³
3^(-2a) = 3³
-2a = 3 /:(-2)
a = -3/2 = -1,5

log a 2 = - ⅓
a^- ⅓ = 2
1 /a^⅓ = 2
a^⅓ = ½ /³
a = (½)³ = ⅛

log₂₇ 81 = x
27^x = 81
3^(3x) = 3⁴
3x = 4 /:3
x = 4/3 = 1⅓

log 0,00001 = x
10^x = 0,00001
10^x = 1/100000
10^x = 1 / 10⁵
10^x = 10⁻⁵
x = -5

log₁₆128 = x
16^x = 128
2^(4x) = 2⁷
4x = 7 /:4
x = ⁷/₄ = 1

log (10⁻⁴)¹² = x
10^x = (10⁻⁴)¹²
10^x = 10⁻⁴⁸
x = -48