Question

PROSZE POMOCY DAJE NAJ​

Answer 1

Odpowiedź:

a )    D = ( 0, + ∞ )

[tex]log x^3 + 2 log x = 3 log x +2 log x = 5 log x = log x^5[/tex]

b)  D =  ( 0 , + ∞ )

log [tex]\sqrt{x} = \frac{3}{2} log x =[/tex]   [tex]log x^{1/2} + log x^{3/2} = log ( x^{1/2}*x^{3/2}) = log x^2[/tex]

c )  D = (  0, +∞ )

[tex]\frac{1}{2} log x^4 + 1 = log (x^4)^{1/2} + log 10 = log x^2 + log 10 = log ( 10 x^2 )[/tex]

d)  D = ( 0, +∞ )

1 - 2 [tex]log[/tex][tex]_{1/2} x =[/tex] 1 - [tex]log_{1/2} x^2 =[/tex]   [tex]log_{1/2} \frac{1}{2} - log_{1/2} x^2 = log_{1/2} ( \frac{1}{2 x^2} )[/tex]

e )  D = ( 0, +∞ )

[tex]2 log_3 x + log_3 y + 1 = log_3 x^2 + log_3 y + log_3 3 = log_3 ( x^2*y*3) = log_3 ( 3 x^2*y)[/tex]

f )  D = ( 0, + ∞ )

[tex]\frac{1}{3} log_5 x^3 - 2 log_5 y\sqrt{x} + \frac{1}{2} = log_5 x- log_5 y^2*x + log_5 \sqrt{5} = log_5 \frac{x*\sqrt{5} }{x*y^2} = log_5 \frac{\sqrt{5} }{y^2}[/tex]

g )  D = ( 0, +∞ )

[tex]\frac{1}{2} log_2 x - log_2 y - 2 = log_2 \sqrt{x} - log_2 y - log_2 4 = log_2 \frac{\sqrt{x} }{4 y}[/tex]

Szczegółowe wyjaśnienie: