Question

a, 5^n x 25 = 125^2
b, 3^n x 9^2 = 27^3
c, 2^4 x 4^n = 8^6

Cảm ơn trước ạ!

Answer 1

a) \(5^n.25=125^2\)

\(\Rightarrow5^n.5^2=\left(5^3\right)^2\)

\(\Rightarrow5^n.5^2=5^6\)

\(\Rightarrow5^n=5^6:5^2\)

\(\Rightarrow5^n=5^4\)

\(\Rightarrow n=4\)

Vậy \(n=4.\)

b) \(3^n.9^2=27^3\)

\(\Rightarrow3^n.\left(3^2\right)^2=\left(3^3\right)^3\)

\(\Rightarrow3^n.3^4=3^9\)

\(\Rightarrow3^n=3^9:3^4\)

\(\Rightarrow3^n=3^5\)

\(\Rightarrow n=5\)

Vậy \(n=5.\)

c) \(2^4.4^n=8^6\)

\(\Rightarrow\left(2^2\right)^2.4^n=2^{18}\)

\(\Rightarrow4^2.4^n=\left(2^2\right)^9\)

\(\Rightarrow4^2.4^n=4^9\)

\(\Rightarrow4^n=4^9:4^2\)

\(\Rightarrow4^n=4^7\)

\(\Rightarrow n=7\)

Vậy \(n=7.\)

Chúc bạn học tốt!