Dwa rownania z logarytmami

[Adamusos]

Udowodnij, ze :

a) \(\displaystyle{ log _{ \sqrt[3]{2} }5 log _{125} 8 = 3}\)
b) \(\displaystyle{ log _{ \sqrt[3]{5} }2 log _{ \sqrt[3]{2} }5 =9}\)

[Wicio]

a)\(\displaystyle{ log _{ \sqrt[3]{2} }5 log _{125} 8 = \frac{log_{125}5}{log_{125} \sqrt[3]{2} } log_{125}8=\frac{ \frac{1}{3} }{log_{125} 2^{ \frac{1}{3} } } log_{125}2^{3}=\frac{ \frac{1}{3} }{ \frac{1}{3} log_{125} 2 } 3log_{125}2=3}\)