Question

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

2
2

16
16

−12
negative Start Fraction 1 over 2 End Fraction

12
Start Fraction 1 over 2 End Fraction

Answer 1

To solve the equation \( 4^{14x} = 4^{34} \) using the laws of exponents, we can equate the exponents since the bases are the same.

1. Set the exponents equal to each other:
\[
14x = 34
\]

2. Divide both sides by 14 to solve for \( x \):
\[
x = \frac{34}{14} = \frac{17}{7}
\]

Now, let's express this in decimal form:
\[
\frac{17}{7} = 2.42857... \approx 2
\]

Since the answer choices you provided don't seem to exactly match what we just derived, let's reassess how to approach this matching approximation.

However, the correct mathematical solution yields:
\[
x = \frac{17}{7}
\]

Among the provided responses, it is closest to 2, but not exactly matching any option. If you're looking for the solution as per your provided options, the closest approximation derived from the answer choices would be 2.

So the answer is:
**2**