Question

Calculati in functie de x, x=log in baza 2 din 3:
log in baza 2/3 din 8/9.
Vă rog frumos!

Answer 1

$x = \log_{2}3=\dfrac{\lg 3}{\lg 2}\\ \\ \\\\\log_{\frac{2}{3}}\frac{8}{9} = \dfrac{\lg\frac{8}{9}}{\lg \frac{2}{3}}=\dfrac{\lg 8-\lg 9}{\lg 2-\lg 3}=\dfrac{3\lg 2-2\lg 3}{\lg 2-\lg 3}^{^{^{\displaystyle (\lg 2}}} = \\ \\ \\ =\boxed{\dfrac{3-2x}{1-x}}$