zadanie 653. Oblicz wartosc b i zadanie 654. Oblicz wartosc a:

[latex]653. D:b>0\a) log_3b=3; b=3^3; b=27\\b) log_frac{1}{5}b=2; b=(frac{1}{5})^2; b=frac{1}{25}\\c) log_7b=-1; b=7^{-1}; b=frac{1}{7}\\d)log_frac{3}{4}b=-2; b=(frac{3}{4})^{-2}; b=(frac{4}{3})^2; b=frac{16}{9}; b=1frac{7}{9}\\e) logb=frac{1}{3}; b=10^frac{1}{3}; b=sqrt[3]{10}\\f) logb=-3; b=10^{-3}; b=0,001\\g) lnb=frac{2}{3}; b=e^frac{2}{3}; b=sqrt[3]{e^2}\\h) lnb=-frac{1}{2}; b=e^{-frac{1}{2}}; b=frac{1}{sqrt{e}}; b=frac{sqrt{e}}{e}[/latex] [latex]654. D:a>0 wedge a eq1\\a) log_a25=2; a^2=25; a=sqrt{25}; a=5\\b) log_a6=-1; a^{-1}=6; a=frac{1}{6}\\c) log_a8=frac{1}{2}; a^frac{1}{2}=8; a=8^2; a=64\\d) log_a2=-frac{1}{3}; a^{-frac{1}{3}}=2; a^frac{1}{3}=frac{1}{2}; a=(frac{1}{2})^3; a=frac{1}{8}\\e) log_asqrt[6]3=frac{1}{3}; a^frac{1}{3}=3^frac{1}{6}; a=(3^frac{1}{6})^3; a=3^frac{1}{2}; a=sqrt3\\f) log_afrac{1}{64}=-3; a^{-3}=frac{1}{64}; a^3=64; a=sqrt[3]{64}; a=4[/latex] [latex]g) log_afrac{1}{11}=-2; a^{-2}=frac{1}{11}; a^2=11; a=sqrt{11}\\h) log_a2sqrt2=3; a^3=sqrt{2^2cdot2}; a^3=2^frac{3}{2}; a=(2^frac{3}{2})^frac{1}{3}; a=2^frac{1}{2}; a=sqrt2[/latex] ©DRK