Question
What is the range of the logarithmic function y=log8x
?(1 point)
Responses
0<y<∞
0 less than y less than infinity
8<y<∞
8 less than y less than infinity
−∞<y<∞
negative infinity less than y less than infinity
−∞<y<0
?(1 point)
Responses
0<y<∞
0 less than y less than infinity
8<y<∞
8 less than y less than infinity
−∞<y<∞
negative infinity less than y less than infinity
−∞<y<0
Answers
GPT-4o mini
To find the range of the logarithmic function \( y = \log_8 x \), we need to consider the properties of logarithmic functions.
1. The logarithmic function is defined for \( x > 0 \).
2. As \( x \) approaches 0 from the positive side, \( y = \log_8 x \) approaches \(-\infty\).
3. As \( x \) increases towards positive infinity, \( y \) also increases without bound towards \(\infty\).
Therefore, the range of the function \( y = \log_8 x \) is:
\[
-\infty < y < \infty
\]
The correct response is:
**−∞<y<∞**
1. The logarithmic function is defined for \( x > 0 \).
2. As \( x \) approaches 0 from the positive side, \( y = \log_8 x \) approaches \(-\infty\).
3. As \( x \) increases towards positive infinity, \( y \) also increases without bound towards \(\infty\).
Therefore, the range of the function \( y = \log_8 x \) is:
\[
-\infty < y < \infty
\]
The correct response is:
**−∞<y<∞**