If $$ 3^{-3 x+6}=27^{x+4} $$, then $$ x $$ equals a.) -2 c.) 5 b.) 1 d.) 0.5

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We start with the equation
  3^(–3x + 6) = 27^(x + 4).

Notice that 27 can be written as 3³, so we have:
  3^(–3x + 6) = (3³)^(x + 4) = 3^(3(x + 4)) = 3^(3x + 12).

Since the bases are the same, the exponents must be equal:
  –3x + 6 = 3x + 12.

Now, solve for x:
  –3x – 3x = 12 – 6
  –6x = 6,
  x = –1.

This shows that x = –1. However, the choices provided are:
  a.) –2  b.) 1  c.) 5  d.) 0.5

Since –1 is not among the given options, there appears to be a discrepancy between the correct answer and the provided choices.
The correct value of $$ x $$ is –1, but none of the provided options match this value.

If \( 3^{-3 x+6}=27^{x+4} \), then \( x \) equals a.) -2 c.) 5 b.) 1 d.) 0.5

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