Question

Дано: log (b)8=c, log(a)81=a, a^c=27. найти: b^a

Answer 1

$log_b8=c, \ log_a81=a, \ a^c=27 \\ log_a81=a \\ \frac{4}{3}log_a27=a \\ \frac{4}{3}log_aa^c=a \\ log_aa^ \frac{4c}{3}=a \\ a^a=a^ \frac{4c}{3} \\ a= \frac{4c}{3} \\ b^a=b^ \frac{4c}{3}= b^ \frac{4log_8}{3}=b^ \frac{12log_b2}{3}=b^{log_b16}=16$
Ответ 16