Question

Daca a= lg 2 si b= lg 3. Calculati

Answer 1

Răspuns:

Explicație pas cu pas:

$a=lg2,~b=lg3,~~x=3^{log_{27}(lg150)^{3}}=3^{3*log_{3^3}lg150}=3^{3*\frac{1}{3} log_3lg150}=3^{log_3lg150}=lg150=lg(6*25)=lg6+lg25=lg(2*3)+lg\frac{100}{4}=lg2+lg3+lg100-lg4= a+b+2-lg2^2=a+b+2-2*lg2=a+b+2-2a=2+b-a.$

Deci x=2+b-a.