Question

Rezolvati in R ecuatia
5·3ˣ=3·5ˣ

Answer 1

$5*3^{x} = 3*5^{x}$

$\ln \left(5\cdot \:3^x\right)=\ln \left(3\cdot \:5^x\right)$$\ln \left(5\right)+x\ln \left(3\right)=\ln \left(3\right)+x\ln \left(5\right)$$x\ln \left(3\right)-\ln \left(5\right)x=\ln \left(\frac{3}{5}\right)$$\frac{\left(\ln \left(3\right)-\ln \left(5\right)\right)x}{\ln \left(3\right)-\ln \left(5\right)}=\frac{\ln \left(\frac{3}{5}\right)}{\ln \left(3\right)-\ln \left(5\right)}$$x=-\frac{\ln \left(\frac{3}{5}\right)}{\ln \left(\frac{5}{3}\right)}$