Odpowiedź:
a) dbca
b) dacb
Pełne rozwiązanie:
[tex]log_{a} b=c[/tex] -----> [tex]a^{c} =b[/tex]
a)
a [tex]2^{x} =64[/tex], x = 6;
b [tex]3^{x} =81[/tex], x = 4;
c [tex]4^{x} =1024[/tex]; x = 5;
d [tex]5^{x} =125[/tex], x = 3;
b)
[tex]x^{\frac{y}{z} } =\sqrt[z]{x^{y} }[/tex]
a [tex]2^{x} =2\sqrt{2}[/tex], [tex]2\sqrt{2} = \sqrt{8} =8^{\frac{1}{2} }[/tex], [tex]8 = 2^{3}[/tex], zatem:
a [tex]2^{x} =2^{\frac{3}{2} }[/tex], [tex]x = \frac{3}{2}[/tex]; (na tej samej zasadzie pozostałe podpunkty)
b [tex]3^{x} =3^{2} *3^{\frac{1}{3} } =3^{2\frac{1}{3} }[/tex], [tex]x = 2\frac{1}{3}[/tex]
c [tex]4^{x} = 32 = 16 * 2 = 4^{2} * 4^{\frac{1}{2} } =4^{2\frac{1}{2} }[/tex], [tex]x = 2\frac{1}{4}[/tex]
d [tex]5^{x} =0,04=\frac{4}{100} =\frac{1}{25} =5^{-2}[/tex], [tex]x = -2[/tex]
