Question

Найдите при каком значение n верно равенство 9^n+2 / 81^n * 3^n+3=1

Answer 1

$\frac{9 ^{n+2} }{81 ^{n}*3 ^{n+3} } =1\\\\ \frac{(3 ^{2} ) ^{n+2} }{(3 ^{4}) ^{n} *3 ^{n+3} } =1\\\\ \frac{3 ^{2n+4} }{3 ^{4n}*3 ^{n+3} } =1\\\\3 ^{2n+4-4n-n-3}=1\\\\3 ^{1-3n}=3 ^{o}\\\\1-3n=0\\\\3n=1\\\\n= \frac{1}{3}$