anonymous
  • anonymous
A student is solving the equation 81^x – 1 = 3^x + 2 Step 1: 81x – 1 =3x + 2 Step 2: (34)x – 1 = 3x + 2 Step 3: 34x – 4 = 3x + 2 Which is the next step? x – 1 = x + 2 4x – 4 = x + 2 4x – 4 = –(x + 2) 4(x – 1) = 3(x + 2)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
OK. I'm assuming that the exponent on the LHS is (x-1). and the exponent on the RHS is x +2. So, ((3)^4)^(x-1) = 3^(x+2) Now you have both sides to the same base so you can equate the exponents 4x-4 = x+2. Adding 4 to both sides and subtracting x from both sides this gives you 3x = 6 or x = 2 -------> and this checks.
anonymous
  • anonymous
81^x -1 = 3^x + 2 OR 3^4x = 3^(x + 3) whence 4x = x + 3 OR x = 1
anonymous
  • anonymous
so would it be the 1st one

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anonymous
  • anonymous
anonymous
  • anonymous
no
anonymous
  • anonymous
\[3^{4x-4}=3^{x+2}\iff 4x-4=x+2\]

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