Zadanie 1.96
Oblicz
a) log_{2\sqrt2}16
(2\sqrt2)^x=16
2*2^{\frac{1}{2}}=2^4
2^{\frac{3}{2}x}=2^4
\frac{3}{2}x=4/*2
3x=8
x=\frac{8}{3}=2\frac{2}{3}
log_{2\sqrt2}16=2\frac{2}{3}
b)
log_{\sqrt3}9\sqrt3=x
(\sqrt3)^x=9\sqrt3
(\sqrt3)^x=3^2*3^{\frac{1}{2}}
(3^{\frac{1}{2}})^x=3^{\frac{4+1}{2}}
3^{\frac{1}{2}x}=3^{\frac{5}{2}}
\frac{1}{2}x=\frac{5}{2}/*2
x=5
c)
log_{\frac{1}{5}}5\sqrt5=log_{\frac{1}{5}}5^1*5^{\frac{1}{2}}=log_{\frac{1}{5}}5^{\frac{3}{2}}=log_{\frac{1}{5}}(\frac{1}{5})^{-\frac{3}{2}}=-\frac{3}{2}=-1,5