Lg2=a lg3=b найти lg1/15

lg[latex] \frac{1}{15} [/latex] = -lg15 = -lg(3·5) = -lg3 - lg5 = -b - lg(3+2) = -b - lg([latex] 10^{a} [/latex] + [latex] 10^{b} [/latex]) lg2 = a ⇒ [latex] 10^{a} [/latex] =2; lg3 = b ⇒ [latex] 10^{b} [/latex] =3

lg(1/15)=-lg3-lg5=-b-lg(10/2)=-b-1+lg(2)=a-b+1