Solve x13<45

Question

.(1 point)
Responses

x<465
x less than Start Fraction 4 over 65 End Fraction

x<1345
x less than 13 Start Fraction 4 over 5 End Fraction

x<1025
x less than 10 Start Fraction 2 over 5 End Fraction

x>525

Answer 1

To solve the inequality \( x^{13} < 45 \), we first take the 13th root of both sides.

This gives us:

\[ x < 45^{1/13} \]

Calculating \( 45^{1/13} \) approximately, we find that:

\[ 45^{1/13} \approx 1.5 \]

Thus, the solution to the inequality is:

\[ x < 1.5 \]

From the options provided, none seem to directly match this result exactly. However, let's break down the provided choices to determine if they correspond to this result:

1. x < 465: This is much larger than 1.5.
2. x < 1345: This is also much larger than 1.5.
3. x < 1025: This is still much larger than 1.5.
4. x > 525: This is incorrect as it suggests x is greater than a large value.

None of the responses correctly articulate the derived condition \( x < 45^{1/13} \approx 1.5 \). If you have to choose among the existing options, please check if there might have been a typographic error, or if you can approximate to the most reasonable value. However, mathematically, the solution remains \( x < 45^{1/13} \).