Log_2 (x-1) ^2 - log_0,5 (x-1) = 9

Log2 (x-1) ^2=2log2 (x-1) = 2log0,5 (x-1) / log0.5 (2)

тогда 2log0,5 (x-1) / log0.5 (2) - log0.5 (x-1) = 9

(2log0.5 (x-1) - log0.5 (2) * log0.5 (x-1)) / log0.5 (2) = 9

log0.5 (x-1) (2-log0.5 (2)) / log0.5 (2) = 9

log0.5 (x-1) (log0.5 (0.5^3)) / log0.5 (2) = 9

3log0.5 (x-1) / log0.5 (2) = 9

3log2 (x-1) = 9

log2 (x-1) = 3

log2 (x-1) = log2 (8)

x-1=8

x=9

ответ: 9