Rozwiąż równanie [latex] log 5+log(x+10)-1=log(21x-20)-log(2x-1)[/latex]

[latex] log frac{5(x+10)}{10} = log frac{21x - 20}{2x - 1} [/latex] [latex] frac{x+10}{2} = frac{21x - 20}{2x - 1} \ (x+10)(2x-1)=2(21x-20) \ 2 x^{2} -x+20x-10=42x-40 \ 2 x^{2} +19x-10-42x+40=0 \ 2 x^{2} -23x+30=0 \ [/latex] [latex] delta=23^{2}-4*2*30=529-240=289= 17^{2} \ x1= frac{23-17}{4} = frac{6}{4} =1,5 \ x2= frac{23+17}{4} = frac{40}{4} =10[/latex]

log[5(x+10)]-log10=log[(21x-20)/(2x-1)], zal. x>20/21  log[5(x+10)/10]=log[(21x-20)/(2x-1) (x+10)/2=(21x-20)/(2x-1)    /*2(2x-1) (x+10)(2x-1)=2(21x-20) 2x²-x+20x-10=42x-40 2x²+19x-42x-10+40=0 2x²-23x+30=0 2x²-20x-3x+30=0 2x(x-10)-3(x-10)=0 (x-10)(2x-3)=0 x-10=0  v  2x-3=0 x=10  v  x=3/2 Odp. x∈{1,5 , 10}