Odpowiedzi

2009-12-10T18:27:31+01:00
5^{\log x}+x^{\log5}=50

Założenia: x>0.

\large 5^{\frac{\log_5x}{\log_510}}+x^{\log5}=50

\large (5^{\log_5x})^{\frac{1}{\log_510}} +x^{\log5}=50

x^{\frac{1}{\log_510}} +x^{\log5}=50

x^{\log_{10}5} +x^{\log5}=50

2\cdot x^{\log5}=50

x^{\log5}=25

x^{\log5}=\log25

\log5\cdot \log x= 2\cdot \log5

\log x=2

x=10^2