Question

Which of the following statements is NOT true about logarithms?

a. If the odds ratio is greater than 1, the log odds ratio is positive
b. When the odds ratio equals 1, the probability of success equals to 0.5
c. If the probability of success is smaller than the probability of failure, the log odds ratio is negative
d. We can take the log of any number

Answer 1

The statement that we can take the log of any number is not true. Logarithms are only defined for positive numbers, and cannot be zero or negative.

Step-by-step explanation:

The statement that is NOT true about logarithms is option d: We can take the log of any number. This is not true because logarithms are only defined for positive numbers. No logarithm can have a zero or negative number as its argument. The common logarithm of a number is the power to which 10 must be raised to equal that number. For example, log(100) is 2 because 10 must be raised to the power of 2 to equal 100. Furthermore, it's important to note:

• The logarithm of a product of two numbers is the sum of the logarithms of those two numbers (log(xy) = log(x) + log(y)).
• The logarithm of a number divided by another number is the difference between the logarithms of those two numbers (log(x/y) = log(x) - log(y)).
• The logarithm of a number raised to an exponent is the product of that exponent and the logarithm of the number (log(x^n) = n*log(x)).
• The common logarithm of a number less than 1 has a negative value.

Therefore, the correct statement is that if the odds ratio equals 1, the log odds ratio is zero, not positive or negative.