Question

Which expressions are equivalent to the one below? Check all that apply.3xA.B.C.x3D.E.3 • 3x - 1F.3 • 3x + 1

Answer 1

Solution

- The solution steps are given below:

$\begin{gathered} \frac{18^x}{3}=\frac{(6\times3)^x}{3}=\frac{6^x\times3^x}{3} \\ =6^x\times3^{x-1}\ne3^x \\ \\ \\ (\frac{18}{6})^x=3^x\text{ \lparen OPTION B\rparen} \\ \\ \\ x^3\ne3^x,\text{ except }x=3. \\ \\ \\ \frac{18^x}{6^x}=(\frac{18}{6})^x=3^x\text{ \lparen OPTION D\rparen} \\ \\ \\ 3.3^{x-1}=3\times\frac{3^x}{3}=3^x\text{ \lparen OPTION E\rparen} \\ \\ \\ 3.3^{x+1}=3\times3^x\times3=3^x\times3^2=3^{x+2}\ne3^x \end{gathered}$

Final Answer

The answers are:

OPTION B

OPTION D

OPTION E