Question

Log √3_(х-2)*log 5_х=2 log3_(х-2)

Answer 1

$log _{ 3^{1/2} } (x-2)*log _{5}x=2log _{3}(x-2)$
$1/2*log _{ 3} (x-2)*log _{5}x=2log _{3}(x-2)$
$1/2*log _{ 3} (x-2)*log _{5}x-2log _{3}(x-2) =0$
$1/2*log _{ 3} (x-2)*(log _{5}x-4) =0$
$log _{ 3} (x-2)*(log _{5}x-4) =0$
$log _{ 3} (x-2)=0$
х-2=1
х=3
$log _{5}x-4 =0$
$log _{5}x =4$
х=5⁴
х=625

Answer 2

Решение во вложении----------------------------