Question

Solve (3x)^(log(3))=(4x)^(log(4))

Answer 1

Log as log base 10

Answer 2

enjoy, friend. hihi

Answer 3

\[3^{\log 3}x^{\log 3}=4^{\log 4}x^{\log 4}\\
\frac{x^{\log 3}}{x^{\log 4}}=\frac{4^{\log 4}}{3^{\log 3}}\\
x^{\log 3-\log 4}=\frac{4^{\log 4}}{3^{\log 3}}\\
(\log 3-\log 4)\log x=\log(4^{\log 4})-\log(3^{\log 3})\\
\log x=\frac{(\log 4)^2-(\log 3)^2}{\log 3-\log 4}\\
\log x=\frac{(\log 4-\log 3)(\log 4+\log 3)}{\log 3-\log 4}\\
\log x=-(\log 4+\log 3)=-\log 12=\log {12^-1}\\
x = 12^{-1}\implies \boxed{x={1\over 12}}
\]

Answer 4

@Hoa I did thoroughly... :-)

Answer 5

amazing!!! how patient you are. hand off

Answer 6

and yet no medals!!!!!