Question

Use the laws of exponents to solve for x in the equation 414x=434
4
1
4
𝑥
=
4
3
4
.(1 point)
Responses

−12
−
1
2
negative Start Fraction 1 over 2 End Fraction

12
1
2
Start Fraction 1 over 2 End Fraction

2
2

16

Answer 1

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

So, we have:

\[
14x = 34
\]

Next, divide both sides by 14 to isolate \( x \):

\[
x = \frac{34}{14}
\]

Now, simplify \( \frac{34}{14} \):

\[
x = \frac{17}{7}
\]

None of the provided responses match \( \frac{17}{7} \). Would you like to double-check the equation or choices?