Question

Решите уравнение lg^2x-5lg x+4=0; 8 log х по основ.2=5 log 8 по основ.5

Answer 1

$OD3:x\ \textgreater \ 0\\lg^2x-5lg x+4=0\\lg^2x-lgx-4lgx+4=0\\lgx(lgx-1)-4(lgx-1)=0\\(lgx-1)(lgx-4)=0\\lgx-1=0\ \ \ \ \ \ \ \ lgx-4=0\\lgx=1\ \ \ \ \ \ \ \ \ \ \ \ \ lgx=4\\x_1=10\ \ \ \ \ \ \ \ \ \ \ \ \ x_2=10000$

$8^{log_2x}=5^{log_58}\\8^{log_2x}=8\\log_2x=1\\x=2$