Question

Answer 1

c: \(\frac{32^{2n}}{11^{2n}}=81\)

=>\(\left(\frac{32}{11}\right)^{2n}=81\)

=>\(2n=\log_{\left(\frac{32}{11}\right)}81\)

=>\(n=\frac12\cdot\log_{\frac{32}{11}}81\)

f: \(\frac{135}{3^{n-2}}=5\)

=>\(3^{n-2}=\frac{135}{5}=27=3^3\)

=>n-2=3

=>n=5

i: \(\frac{3^5}{3^{n}}=3^{10}\)

=>\(3^{5-n}=3^{10}\)

=>5-n=10

=>n=-5

l: \(3^{x}=\frac{9^8}{27^3\cdot81^2}\)

=>\(3^{x}=\frac{3^{16}}{3^9\cdot3^8}=\frac13=3^{-1}\)

=>x=-1