Question
What must be the smallest value of k so that 3.54×10k becomes larger than 3.54×104 ?(1 point) k =
Answers
GPT-4o mini
To find the smallest value of \( k \) such that \( 3.54 \times 10^k \) is larger than \( 3.54 \times 10^4 \), we can set up the inequality:
\[
3.54 \times 10^k > 3.54 \times 10^4
\]
Since both sides have the same coefficient (3.54), we can divide both sides by 3.54 (assuming it's not zero):
\[
10^k > 10^4
\]
To compare the powers of 10, we can rewrite this as:
\[
k > 4
\]
The smallest integer value of \( k \) that satisfies this inequality is:
\[
k = 5
\]
Thus, the smallest value of \( k \) is \( \boxed{5} \).
\[
3.54 \times 10^k > 3.54 \times 10^4
\]
Since both sides have the same coefficient (3.54), we can divide both sides by 3.54 (assuming it's not zero):
\[
10^k > 10^4
\]
To compare the powers of 10, we can rewrite this as:
\[
k > 4
\]
The smallest integer value of \( k \) that satisfies this inequality is:
\[
k = 5
\]
Thus, the smallest value of \( k \) is \( \boxed{5} \).