Question

log _{frac{3}{2}} left( {x^2 - 3x} right) = 8

Answer 1

$\log _{frac{3}{2}} ( {x^2 - 3x}) = 8\ left(frac{3}{2}right)^8=x^2-3x\ frac{6561}{256}=x^2-3x\ x^2-3x-frac{6561}{256}=0|cdot 256\ 256x^2-768-6561=0\\ Delta=(-768)^2-4cdot256cdot(-6561)\ Delta=589824+6718464\ Delta=7308288\ sqrtDelta=96sqrt{793}\ \ x_1=frac{-(-768)-96sqrt{793}}{2cdot256}\ x_1=frac{768-96sqrt{793}}{512}\ x_1=frac{3}{16}(8-sqrt{793})\\ x_2=frac{-(-768)+96sqrt{793}}{2cdot256}\ x_2=frac{768+96sqrt{793}}{512}\ x_2=frac{3}{16}(8+sqrt{793})$