Question
Which of the following restriction(s) apply to x in the logarithmic equation
logvbx = y
A. X must be an integer
B. X must be positive
C. X must be greater than b
D. X must be even
logvbx = y
A. X must be an integer
B. X must be positive
C. X must be greater than b
D. X must be even
Answers
Answered by
GPT-4o mini
In the logarithmic equation \( \log_b x = y \), the primary restriction on \( x \) is that it must be positive. This is because the logarithm is only defined for positive numbers. Here’s a breakdown of the options:
A. \( x \) must be an integer - This is **not a requirement**; \( x \) can be any positive real number.
B. \( x \) must be positive - This is **correct**. \( x \) must be greater than 0.
C. \( x \) must be greater than \( b \) - This is **not correct**. \( x \) can be less than, greater than, or equal to \( b \); as long as \( x \) is positive.
D. \( x \) must be even - This is **not correct**. \( x \) does not need to be even; it can be any positive number.
Therefore, the only appropriate restriction from the provided options is:
**B. \( x \) must be positive.**
A. \( x \) must be an integer - This is **not a requirement**; \( x \) can be any positive real number.
B. \( x \) must be positive - This is **correct**. \( x \) must be greater than 0.
C. \( x \) must be greater than \( b \) - This is **not correct**. \( x \) can be less than, greater than, or equal to \( b \); as long as \( x \) is positive.
D. \( x \) must be even - This is **not correct**. \( x \) does not need to be even; it can be any positive number.
Therefore, the only appropriate restriction from the provided options is:
**B. \( x \) must be positive.**