Question

Wiedząc że log₁₂4=a wyraź w zależności od a liczby:
a) log₁₂48
b) log₁₂3
c) log₁₂27
d) log₁₂1/4√3

Proszę o pomoc i rozwiązanie z wytłumaczeniem

Answer 1

log 12 [ 4] = a

zatem

a)

log 12 [ 48] = log 12 [ 12*4] = log 12 [ 12] + log 12 [4] = 1 + a

b)

log 12 [ 3 ] = log 12 [ 12/4] = log 12 [ 12 ] - log 12 [ 4] = 1 - a

c)

log 12 [ 27 ] = log 12 [ 3^3 ] = 3 * log12 [3 ] = 3 *(1 - a)

d)

log 12 [ 1 /( 4 p(3)] = log 12 [1 ] - log 12 [ 4 p(3)] =

=  0 - [ log 12[4] + log 12 [ p(3)] = - [ a +  log 12 [ 3 ^(1/2)] ] =

= - [ a + (1/2) *log 12 [ 3 ]] = - a - (1/2)*(1 - a) = - a  - 1/2 + (1/2) a =

= - (1/2)a - 1/2  = ( -1/2)*(a + 1)

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