Question

Решите и получите 50 баллов!!

Answer 1

$log_frac{1}{2}(7x-1)=-3, \ left { {{7x-1 textgreater 0,} atop {7x-1=(frac{1}{2})^{-3};}} right. left { {{x textgreater frac{1}{7},} atop {7x-1=8;}} right. left { {{x textgreater frac{1}{7},} atop {7x=9;}} right. left { {{x textgreater frac{1}{7},} atop {x=1frac{2}{7};}} right. \ x=1frac{2}{7};$

$log_4(5-6x)=2,\ left { {{5-6x textgreater 0,} atop {5-6x=4^2;}} right. left { {{ x textless frac{5}{6},} atop {5-6x=16;}} right. left { {{ x textless frac{5}{6},} atop {6x=-11;}} right. left { {{ x textless frac{5}{6},} atop {=-1frac{5}{6};}} right. \ x=-1frac{5}{6};$

$log_416+log_749-log_327=log_44^2+log_77^2-log_33^3=\=2log_44+2log_77-3log_33=2+2-3=1.$