Question

Which equation is equivalent to (one-third) Superscript x Baseline = 27 Superscript x + 2? 3 Superscript x Baseline = 3 Superscript negative 3 x + 2 3 Superscript x Baseline = 3 Superscript 3 x + 6 3 Superscript negative x Baseline = 3 Superscript 3 x + 2 3 Superscript negative x Baseline = 3 Superscript 3 x + 6

Answer 1

Answer:

C 3 Superscript x Baseline = 3 Superscript 3 x + 6 3 Superscript negative x Baseline

Step-by-step explanation:

Answer 2

Answer:

Option D : 3 Superscript negative x Baseline = 3 Superscript 3 x + 6

Step-by-step explanation:

Let us first convert all the equations in Mathematical form for readability.

The question equation will become:

$(\frac{1}{3})^{x}=(27)^{x+2}$        ----------------- (1)

And the option equations will be:

A.   $3^{x}=3^{(-3x+2)}$

B.   $3^{x}=3^{(3x+6)}$

C.   $3^{-x}=3^{(3x+2)}$

D.   $3^{-x}=3^{(3x+6)}$

Now, let's solve the question equation. Simplifying equation (1), we get

$(3^{-1})^{x} = (3^3)^{x+2}\\\\3^{-x} = 3^{3(x+2)}\\\\3^{-x} = 3^{(3x+6)}$

Hence, option D is correct.