Question

oblicz:

log₂ √2 l

og₃ ³√3=⅓

log₄ ⁵√16=5

log₃ ³√9

log₂ √½

log₅ ⁵√25

log₅ 5√5

log₉ 3³√3

log₃ 54+log₃ 1,5

log₂ 144-log₂ 9

log₂ 5+ log₂ 5,6

2log₃ 6-log₃ 4

log₄ 20-log₄ 5

log₅ 0,5+2log₅ 20- 3log₅ 2

log20 - log2

log40-log40000

Answer 1

log 2 [ p(2)] = 1/2  , bo   2^(1/2) = p(2)

log 3 [ p3st (3)] = log 3 [ 3^(1/3)] = 1/3

log 4 [ p5st (16 )] = log 4 [ 16^(1/5)] = log 4 [ (4^2)^(1/5)] = log 4[4 ^(2/5)] =

(2/5) *log 4 [4] = (2/5)*1 = 2/5

log 3 [ p3st (9)] = log 3 [ 9^(1/3)] = log 3 [ (3^2)^(1/3)] = log 3 [3 ^(2/3)] =

= (2/3) *log 3 [3] = (2/3)*1 = 2/3

log 2 [ p(1/2)] = log 2 [ 1/ p(2)] = log 2 [ p(2)^(-1)] = log 2 [ (2^(1/2)^(-1)]

= log 2 [ 2 ^(-1/2)] = (-1/2) log 2 [2] =  (-1/2) *1 = - 1/2

log 5 [ p5st (25)] = log 5 [ 25^(1/5)] = log 5 [ (5^2)^(1/5)] = log 5 [ 5^(2/5) ] =

= (2/5)*log 5 [ 5] = 2/5

log 5 [ 5 p(5)] = log 5 [ 5* 5^(1/2)] = log 5 [ 5^(3/2)] = (3/2) *log 5 [ 5] = 3/2

log 3 [54 ] + log 3 [1,5] = log 3 [ 54*1,5] = log 3 [81 ] = 4  , bo 3 ^4 = 81

log2 [144] - log 2 [9] = log 2 [144/9] = log 2 [16 ] = 4,  bo 2^4 = 16

log2 [5] + log 2 [5,6 ] = log 2 [ 5*5,6 ] = log 2 [ 28] = log 2[ 4*7] =

= log 2 [2] + log 2 [7] = 1 + log2 [7]

2 log 3 [6] - log 3 [4] = log 3 [ 6^2] - log 3 [4] = log 3 [36] - log 3 [4] =

= log 3 [36/4] = log 3 [ 9] = 2 , bo  3^2 = 9

log 4 [20 ] - log 4 [5] = log 4 [ 20/5] = log 4 [4] = 1

log 5 [ 0,5 ] + 2 log 5 [20 ] - 3 log 5 [2] = log 5[0,5] + log 5[20^2] - log 5 [2^3] =

= log 5 [ 0,5 * 400] - log 5[8] = log 5 [ 200/8] = log 5 [25] = 2,  bo 5^2 = 25

log 20 - log 2 = log [ 20/2 ] = log 10 = 1  , bo 10^1 = 10

log 40 - log 40 000 = log [ 40/40 000 ] = log [ 1/1000] = - 3, bo 10^(-3) = 1/1000

log 9 [ 3 p3st(3)] = log 9 [ 3*3^(1/3)] = log 9 [ 3^(4/3)] = (4/3)*log 9 [3] =

= (4/3) * log 3^2 [ 3] = (4/3)*(1/2)*log 3 [3] = (4/6)*1 = 2/3