Question

Log2/3 9/4=x+3 ????????????????

Answer 1

$log_{\frac{2}{3}}\frac{9}{4}=x^3\\ \\ \left(\frac{2}{3}\right)^x+3=\frac{9}{4}\\ \\ \left(\frac{2}{3}\right)^{x+3}=\left(\frac{2}{3}\right)^{-2}\\ \\ x+3=-2\\ \\ x=-2-3\\ \\ \boxed{x=-5}$

Answer 2

$log_{ \frac{2}{3} } \frac{9}{4} =x+3\\\\log_{ \frac{2}{3} }( \frac{2}{3})^{-2} =x+3\\\\-2=x+3\\\\-x=3+2\\\\-x=5\ /\cdor(-1)\\\\x=-5$