Câu hỏi của Huong Pham

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!

Vũ Minh Tuấn · Accepted Answer

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!Câu trả lời: a) $5^n.25=125^2$