Question

Oblicz logarytmy z zadania

Answer 1

Odpowiedź:

Szczegółowe wyjaśnienie:

a.

[tex]log_2(log10000)=log_2(log10^4)=log_24=log_22^2=2[/tex]

b.

[tex]log_3(log1000)=log_3(log10^3)=log_33=1[/tex]

c.

[tex]log_\frac{1}{9} log1000=log_{9^{-1}}log10^3=log_{3^{-2}}3=-\frac{1}{2} log_33=-\frac{1}{2} *1=-\frac{1}{2}[/tex]

d.

[tex]log_9(log_8(log100))=log_{3^2}(log_{2^3}(log10^2))=\frac{1}{2}log_3(\frac{1}{3} log_22)=\frac{1}{2} log_3(\frac{1}{3} *1) =\\=\frac{1}{2} log_3\frac{1}{3} =\frac{1}{2}log_33^{-1}=\frac{1}{2}*(-1)=-\frac{1}{2}[/tex]

e.

[tex]log_{10}(log_21024)=log(log_22^{10})=log10=1[/tex]      

          (brak podstawy oznacza [tex]loga=log_{10}a[/tex])