Question

$1) frac{ log_{5} 64}{ log_{5} 16} 2) log^2_{2}x-4 log_{2}+3=0$

помогите,пожалуйста!

Answer 1

log(5)64/log(5)16=log(16)64==3/2=1,5

(log(2)x)²-4log(2)x+3=0
log(2)x=a
a²-4a+3=0
a1+a2=4 U a1*a2=3
a1=1⇒log(2)x=1⇒x=2
a2=3⇒log(2)x=3⇒x=8

Answer 2

$frac{log(5)64}{log(5)16} =log(16)64=1,5$

$log^2_2x-4log_2x+3=0 \ log_2x=a \ a^2-4a+3=0 \ a_1=1 \ a_2=3 \ log_2x=1 \ x=2 \ log_2x=3; \ x=8$