Question

[Nguyễn Khánh Ngọc]

(x⁵⁴)²=5¹⁰⁸

(5\(^{ }\)^x)²=125³:5²

Giải cứuuu

Answer 1

[GV Nguyễn Trần Thành Đạt]

\(\left(x^{54}\right)^2=x^{54.2}=x^{108}\\ Mà:\left(x^{54}\right)^2=5^{108}\Leftrightarrow x^{108}=5^{108}=\left(-5\right)^{108}\\ Vậy:x=5.hoặc.x=-5\\ ---\\ \left(5^x\right)^2=125^3:5^2\\ \Leftrightarrow5^{2x}=\left(5^3\right)^3:5^2=5^9:5^2=5^7\\ Vậy:2x=7\\ Vậy:x=\dfrac{7}{2}\)

Answer 2

[Nguyễn Minh Dương]

\(\left(x^{54}\right)^2=5^{108}\\ \Rightarrow x^{108}=5^{108}\)

\(\Rightarrow x=5.\)

\(\left(5^x\right)^2=125^3:5^2\\ \Rightarrow\left(5^x\right)^2=\left(5^3\right)^3:5^2\\ \Rightarrow\left(5^x\right)^2=5^9:5^2\\ \Rightarrow\left(5^x\right)^2=5^7\\ \Rightarrow x.2=5\\ \Rightarrow x=2,5\)