+14923
\(log_{4n}(40\sqrt{3})=log_{3n}(45)\\ find\ n^3\)
Hello Guest!
\(log_{4n}(40\sqrt{3})=log_{3n}(45)=z\)
\((4n)^z=40\sqrt{3}\)
\( (3n)^z=45\) | \(\times\ \frac{(4n)^z}{(3n)^z}=\frac{4^zn^z}{3^zn^z}=(\frac{4}{3})^z\)
\((\frac{4}{3})^z\cdot(3n)^z=45\cdot (\frac{4}{3})^z \)
\(z\cdot ln(4n)=ln(40\cdot \sqrt{3})\\ z=ln(40\cdot \sqrt{3})/ln(4n)\\ z\cdot ln(3n)=ln(45\cdot \sqrt{3})\\ z=ln(45\cdot \sqrt{3})/ln(3n)\)
To be continued.
!
