Question

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)

Answer 1

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.

Answer 2

81^x -1 = 3^x + 2
OR 3^4x = 3^(x + 3) whence 4x = x + 3 OR x = 1

Answer 3

so would it be the 1st one

Answer 4

@satellite73

Answer 5

no

Answer 6

\[3^{4x-4}=3^{x+2}\iff 4x-4=x+2\]