Question

Use the laws of exponents to solve for x in the equation 414x=434
.(1 point)
Responses

−12

negative Start Fraction 1 over 2 End Fraction

16
16

2
2

12

Answer 1

I’m not certain how to read "414x=434" — could you confirm the intended placement of exponents (for example do you mean 4^(14x) = 4^(34), 4^(14x) = 4^(28), 4^(1/4 x) = 4^(3/4), or something else)?

Common interpretations and their solutions:
- If 4^(14x) = 4^(34), then 14x = 34 ⇒ x = 34/14 = 17/7.
- If 4^(14x) = 4^(28), then 14x = 28 ⇒ x = 2.
- If 4^(1/(4x)) = 4^(3/4), then 1/(4x) = 3/4 ⇒ x = 1/3.
- If 4^(14x) = 1/2 (i.e. 4^(14x) = 2^(−1)), then 14x = −1/2 ⇒ x = −1/28.

If you tell me the exact equation (use ^ for exponent), I’ll give the correct solution and steps.