Question

Answer 1

1:

\(5^3=125\)

\(2^{10}=1024;1^{2023}=1\)

\(2023^0=1\)

5:

a: \(5\cdot3^x=405\)

=>3^x=405/5=81

=>x=4

b: 2^x:16=4

=>2^x=64=2⁶

=>x=6

c: (x+3)³=125

=>x+3=5

=>x=2

d: (2x+1)²=81

=>\(\left[{}\begin{matrix}2x+1=9\\2x+1=-9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-5\end{matrix}\right.\)

 

Answer 2

Bài 5:

a) \(5\cdot3^x=405\)

\(\Rightarrow3^x=405:5\)

\(\Rightarrow3^x=81\)

\(\Rightarrow3^x=3^4\)

\(\Rightarrow x=4\)

b) \(2^x:16=4\)

\(\Rightarrow2^x:2^4=2^2\)

\(\Rightarrow2^{x-4}=2^2\)

\(\Rightarrow x-4=2\)

\(\Rightarrow x=2+4\)

\(\Rightarrow x=6\)

c) \(\left(x+3\right)^3=125\)

\(\Rightarrow\left(x+3\right)^3=5^3\)

\(\Rightarrow x+3=5\)

\(\Rightarrow x=5-3\)

\(\Rightarrow x=2\)

d) \(\left(2x+1\right)^2=81\)

\(\Rightarrow\left(2x+1\right)^2=9^2\)

TH1: \(2x+1=9\)

\(\Rightarrow2x=9-1\)

\(\Rightarrow2x=8\)

\(\Rightarrow x=\dfrac{8}{2}\)

\(\Rightarrow x=4\)

TH2: \(2x+1=-9\)

\(\Rightarrow2x=-9-1\)

\(\Rightarrow2x=-10\)

\(\Rightarrow x=-\dfrac{10}{2}\)

\(\Rightarrow x=-5\)