Odpowiedź:
zad2
a)log₃3²⁰=20log₃3=20
b)[tex]log_{5}}5^{0,1}}=0,1log_{5}}5=0,1[/tex]
c)[tex]log_{0,3}}\sqrt{0,3} =log_{0,3}}0,3^{\frac{1}{2} }=\frac{1}{2} log_{0,3}}0,3=\frac{1}{2}[/tex]
d)[tex]log_{\sqrt{3} }\sqrt{3^{10}} =10log_{\sqrt{3} }\sqrt{3} =10[/tex]
e)[tex]4^{log_{4}5=5[/tex]
f)[tex]3^{7log_{3}2=3^{log_{3}2^7=2^7=128[/tex]
g)[tex]25^{log_{5}3}=5^{2log_{5}3}=5^{log_{5}3^2}=3^2=9[/tex]
h)[tex]7^{log_{49}4}}=7^{log_{7^2}4}=7^{\frac{1}{2} log_{7}4}=7^{log_{7}4^{\frac{1}{2}} =4^{\frac{1}{2} }=\sqrt{4} =2[/tex]
zad3
a)[tex]log_{3}\frac{2}{9} +log_{3}\frac{1}{6} =log_{3}(\frac{2}{9} *\frac{1}{6} )\=log_{3}\frac{1}{27} =log_{3}3^{-3}=-3[/tex]
b)[tex]log_{2}10+log_{2}1,6=log_{2}(10*1,6})=log_{2}16=log_{2}2^4=4[/tex]
c)log25+log4=lof(25*4)=log100=log10²=2
d)[tex]log_{5}\sqrt{10} -log_{5}\sqrt{2} =log_{5}\frac{\sqrt{10} }{\sqrt{2} } }=log_{5}\sqrt{5} =log_{5}5^{\frac{1}{2}}=\frac{1}{2}[/tex]
e)[tex]log9-log0,9=log\frac{9}{0,9} =log10=1[/tex]
f)[tex]log_{8}7-log_{8}14=log_{8}\frac{7}{14} =log_{2^3}\frac{1}{2} =\frac{1}{3}log_{2}2^{-1}}=-\frac{1}{3}[/tex]
Szczegółowe wyjaśnienie:
