Log3x=log3 18 -1/4 log3 16 + 2 log3 5 - вопрос №3318143162354950626 от ekaterinaring2017 01.09.2022 10:36

Question

Математика: Log3x=log3 18 -1/4 log3 16 + 2 log3 5

ekaterinaring2017 · Answer

Log_3 x = Log_3 18 -(1/4)Log_3 16 +2Log_3 5 ;
* * * Log_3 x = Log_3 (18*5²/(16^1/4)) ⇒x =225 * * * ;
По шагам:
Log_3 x = Log_3 18 -(1/4)Log_3 2⁴ +Log_3 5² ;
Log_3 x = Log_3 18 -(1/4)*4*Log_3 2 +Log_3 5² ;
Log_3 x = Log_3 18 - Log_3 2 +Log_3 25 ;
Log_3 x = Log_3 (18*25/2) ;
Log_3 x = Log_3 (9*25) ;
x = 9*25 ;
x =225.