Question

[Trần Minh Nguyệt]

tìm số tự nhiên x :
a) 3x4^x+1 - 5x4^x=448
b)5x(x-2)^3=4^3 + 71 với x>1

Answer 1

[Nguyễn Đức Trí]

a) \(3x4^{x+1}-5.4^x=448\)

\(\Leftrightarrow4^x\left(3x4-5\right)=448\)

\(\Leftrightarrow4^x.7=448\)

\(\Leftrightarrow4^x=64=4^3\)

\(\Leftrightarrow x=3\)

b) \(5.\left(x-2\right)^3=4^3+71\left(x>1\right)\)

\(\Leftrightarrow5.\left(x-2\right)^3=64+71\)

\(\Leftrightarrow5.\left(x-2\right)^3=135\)

\(\Leftrightarrow\left(x-2\right)^3=27=3^3\)

\(\Leftrightarrow x-2=3\)

\(\Leftrightarrow x=5\)