Question
1) Use the quotient rule to expand log9(3x)
log
9
(
3
𝑥
)
(1 point)
Responses
3log9x
3
log
9
𝑥
3 log sub 9 x
log9 3log9x
log
9
3
log
9
𝑥
log9 3log9x
log
9
3
log
9
𝑥
log
9
(
3
𝑥
)
(1 point)
Responses
3log9x
3
log
9
𝑥
3 log sub 9 x
log9 3log9x
log
9
3
log
9
𝑥
log9 3log9x
log
9
3
log
9
𝑥
Answers
GPT-4o mini
To expand \( \log_9(3x) \) using the properties of logarithms, we can apply the product rule which states that \( \log_b(mn) = \log_b(m) + \log_b(n) \).
Using this, we have:
\[
\log_9(3x) = \log_9(3) + \log_9(x)
\]
Now, we can express \( \log_9(3) \) in terms of a different base, if needed. \( \log_9(3) \) can also be calculated using the change of base formula, but if we keep it as it is, we find that:
\[
\log_9(3) + \log_9(x)
\]
Therefore, the expression \( \log_9(3x) \) expands to:
\[
\log_9(3) + \log_9(x)
\]
If you require a numerical approximation for \( \log_9(3) \) or a further expansion, please let me know!
Using this, we have:
\[
\log_9(3x) = \log_9(3) + \log_9(x)
\]
Now, we can express \( \log_9(3) \) in terms of a different base, if needed. \( \log_9(3) \) can also be calculated using the change of base formula, but if we keep it as it is, we find that:
\[
\log_9(3) + \log_9(x)
\]
Therefore, the expression \( \log_9(3x) \) expands to:
\[
\log_9(3) + \log_9(x)
\]
If you require a numerical approximation for \( \log_9(3) \) or a further expansion, please let me know!