Wzory
log(a) + log(b) = logab
log(a) = log(b) ⇔ a = b
Rozwiązanie
log_9(x-3)+log_9(3x-2)=log_918
log_9(x-3)(3x-2)=log_918
(x-3)(3x-2)=18
3x^2-2x-9x+6=18
3x^2-11x-12=0
a=1 , b=-11 , c=-12
\Delta=b^2-4ac=(-11)^2-4\cdot 3 \cdot (-12)=121+144=265
\sqrt\Delta=\sqrt{265}
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-(-11)-\sqrt{265}}{2\cdot 3}=\frac{11-\sqrt{265}}{6}
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-(-11)+\sqrt{265}}{2\cdot 3}=\frac{11+\sqrt{265}}{6}
x\in \{\frac{11-\sqrt{265}}{6} \ , \ \frac{11+\sqrt{265}}{6} \}