oblicz

[snowinska91]

a) 49\(^{log_7 5}+27^{log_3 4}+2^{log_2 5}\)
b)\(( \sqrt{5})^{log_5 16}-( \sqrt{7})^{log_7 6}\)
c)\(5^{3-log_5 2}\)
d)\(5^{2-log_5 9}\)

[eresh]

a) 49\(^{log_7 5}+27^{log_3 4}+2^{log_2 5}\)

\(49^{\log_7 5}+27^{\log_3 4}+2^{\log_2 5}=7^{2log_7 5}+3^{3\log_3 4}+2^{\log_2 5}=7^{log_7 25}+3^{\log_3 64}+2^{\log_2 5}=25+64+5=94\)

[eresh]

b)\(( \sqrt{5})^{log_5 16}-( \sqrt{7})^{log_7 6}\)

\(( \sqrt{5})^{\log_5 16}-( \sqrt{7})^{\log_7 6}=5^{0,5\log_5 16}-7^{0,5\log_7 6}=5^{\log_54}-7^{\log_7\sqrt{6}}=4-\sqrt{6}\)

[eresh]

c)\(5^{3-log_5 2}\)
d)\(5^{2-log_5 9}\)

\(5^{3-\log_5 2}=5^3\cdot 5^{-\log_52}=125\cdot 5^{\log_50,5}=125\cdot 0,5=\frac{125}{2}\)


\(5^{2-\log_5 9}=5^2\cdot 5^{-\log_59}=25\cdot 5^{\log_5\frac{1}{9}}=25\cdot\frac{1}{9}=\frac{25}{9}\)