Question

sa se exprime în funcție de a ​

Answer 1

Răspuns:

Explicație pas cu pas:

b) log₁₅75 = ?  a = log₃45

log₁₅75 = log₃75 / log₃15 = log₃(3·5²) / log₃(3·5) =

= (log₃3 + log₃5²) / (log₃3 + log₃5) = (1 + 2log₃5)/(1+log₃5)

log₃45 = log₃(3²·5) = 2log₃3 + log₃5 = 2 + log₃5 = a =>

log₃5 = a-2 => log₃75 = [1+2(a-2)]/(1+a-2) = (1+2a-4)/(a-1) =

= (2a-3)/(a-1)

d) log₂₈98 = ? ; a = log₁₁₂56

log₁₁₂56 = log₁₁₂(112/2) = log₁₁₂112 - log₁₁₂2 = 1 - log₁₁₂2 = a =>

log₁₁₂ = 1-a

log₁₁₂56 = log₁₁₂(7·8) = log₁₁₂7 + log₁₁₂2³ = log₁₁₂7 + 3 log₁₁₂2 =

= log₁₁₂7 + 3(1-a) = a =>

log₁₁₂7 = a-3(1-a) = a-3+3a =>

log₁₁₂7 = 4a-3

log₂₈98 = log₁₁₂98 / log₁₁₂28 = log₁₁₂(7²·2) / log₁₁₂(7·2²) =

= (log₁₁₂7² + log₁₁₂2) / (log₁₁₂7 + log₁₁₂2²) =

= (2log₁₁₂7 + log₁₁₂2) / (log₁₁₂7 + 2log₁₁₂2) =

= [2(4a-3) + 1-a] / (4a-3 + 2-2a) = (8a-6+1-a)/(2a-1) =

= (7a-5)/(2a-1)