Question

Solve. Write your answer as an integer or a fraction in simplest form.
94x–4=
1
81
x–4
x=

Answer 1

I’m not sure how your equation is meant to be formatted. Here are the common interpretations and their solutions — tell me which one matches what you meant.

1) If you meant 94/(x − 4) = (1/81)(x − 4):
- Multiply through: 94 = (1/81)(x − 4)^2
- (x − 4)^2 = 94·81 = 7614
- x = 4 ± 9√94

2) If you meant 94x − 4 = (1/81)x − 4:
- The −4 cancels, so 94x = (1/81)x ⇒ x(94 − 1/81) = 0
- x = 0

3) If you meant 94x − 4 = 1/(81x − 4):
- Multiply: (94x − 4)(81x − 4) = 1 ⇒ 7614x^2 − 700x + 15 = 0
- x = (350 ± √8290)/7614

4) If you meant 94/(x − 4) = 1/(81x − 4):
- Cross-multiply: 94(81x − 4) = x − 4 ⇒ 7613x = 372
- x = 372/7613

Which of these is the equation you intended?