Question
What must be the smallest value of k
so that 3.54×10 k
becomes larger than 3.54×10 4
?(1 point)
so that 3.54×10 k
becomes larger than 3.54×10 4
?(1 point)
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 need to compare the two expressions.
We can divide both sides of the inequality \( 3.54 \times 10^k > 3.54 \times 10^4 \) by \( 3.54 \) (assuming \( 3.54 \) is positive, which it is):
\[
10^k > 10^4
\]
Since both sides are powers of 10, we can equate the exponents:
\[
k > 4
\]
The smallest integer value for \( k \) that satisfies this inequality is:
\[
k = 5
\]
Thus, the smallest value of \( k \) such that \( 3.54 \times 10^k \) becomes larger than \( 3.54 \times 10^4 \) is \( \boxed{5} \).
We can divide both sides of the inequality \( 3.54 \times 10^k > 3.54 \times 10^4 \) by \( 3.54 \) (assuming \( 3.54 \) is positive, which it is):
\[
10^k > 10^4
\]
Since both sides are powers of 10, we can equate the exponents:
\[
k > 4
\]
The smallest integer value for \( k \) that satisfies this inequality is:
\[
k = 5
\]
Thus, the smallest value of \( k \) such that \( 3.54 \times 10^k \) becomes larger than \( 3.54 \times 10^4 \) is \( \boxed{5} \).