Question

5^(x-2)(x+3) = 1^x

Answer 1

\(5^{\left(x-2\right)\left(x+3\right)}=1^x\)

\(\Rightarrow5^{\left(x-2\right)\left(x+3\right)}=1\)

\(\Leftrightarrow5^{\left(x-2\right)\left(x+3\right)}=5^0\)

\(\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0+2\\x=0-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)

Vậy \(x_1=-3;x_2=2\)

Answer 2

Ta có: \(1^x=1\forall x\in R\)

\(\Rightarrow5^{\left(x-2\right)\left(x+3\right)}=1\forall x\in R\)

\(\Rightarrow\left(x-2\right)\left(x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)

Vậy x = 2 hoặc x = -3

Answer 3

Ta có :

\(5^{\left(x-2\right)\left(x+3\right)}=1^x\)

\(\Rightarrow5^{\left(x-2\right)\left(x+3\right)}=1\)

\(\Rightarrow5^{\left(x-2\right)\left(x+3\right)}=5^0\)

\(\Rightarrow\left(x-2\right)\left(x+3\right)=0\) \(\Rightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0+2\\x=0-3\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\) Vậy \(x\in\left\{2;-3\right\}\)

Answer 4

Ta có:1^x=1,thay 1 vào 1^x:

5^(x-2)(x+3)=1

Mà 5⁰=1,thay 5⁰vào 1:
5^(x-2)(x+3)=5⁰

\(\Rightarrow\)(x-2)(x+3)=0

(x-2) hoặc (x+3)=0

+nếu x-2=0

\(\Rightarrow\)x=0+2=2

+nếu x+3=0

\(\Rightarrow\)x=0-3=-3

Vậy x={2;-3}

Answer 5

\(5^{\left(x-2\right)\left(x+3\right)}=1^x\)

\(\Rightarrow5^{\left(x-2\right)\left(x+3\right)}=1\)

\(\Leftrightarrow5^{\left(x-2\right)\left(x+3\right)}=5^0\)

\(\Rightarrow\left(x-2\right)\left(x+3\right)=0\)

\(\Leftrightarrow x-2=0\) hoặc \(x+3=0\)

\(\Rightarrow x=2\) \(\Rightarrow x=-3\)

Vậy \(x=2\) hoặc \(x=-3\)