log3 (2x-3) = 2 log2 (3x-2) = 3

Question

log3 (2x-3) = 2
log2 (3x-2) = 3

Answer 1

log3 (2x-3) = 2
ОДЗ  2x-3 >0; 2x > 3; x >3/2
решение
3^2 = 2x-3
9+3 =2x
2x=12
x=6

log2 (3x-2) = 3
ОДЗ  3x-2 >0; 3x > 2; x >2/3
решение
2^3 = 3x-2
8+2 =3x
3x=10
x=10/3

Answer 2

 log3 (2x-3) = 2                                             log2 (3x-2) = 3
 ОДЗ: 2х-3>0, 2x>3, x>1,5                           ОДЗ: 3x-2>0, 3x>2, x> 2/3
2x-3=3²                                                         3x-2=2³
2x-3=9                                                          3x-2=8
2x=12                                                           3x=10
x=6∈ОДЗ                                                     x=10/3=3 1/3∈ОДЗ
Ответ: 6                                                       Ответ: 3 1/3