Question

Determine whether each statement is true or false. You have one submission for each statement.

a) ln (a+b)=(a) (b) for all ( a, b>0 )
A True
B False
(b) (a * b)=(a)+(b)
A True
B False

Answer 1

The first statement is false and should be corrected to ln(a × b) = ln(a) + ln(b), which is a true property of logarithms. The second statement is true as it correctly describes a logarithm property of multiplication.

Step-by-step explanation:

The statements given are:

1. ln (a + b) = ln(a) × ln(b) for all a, b > 0
2. ln(a × b) = ln(a) + ln(b)

Let's determine the truth value of these statements.

Statement 1 is false. The correct statement would be ln(a × b) = ln(a) + ln(b), which is a property of logarithms that states the logarithm of a product is equal to the sum of the logarithms.

Statement 2 is true. This is indeed a property of logarithms that explains how the logarithm of a product can be expressed as the sum of the logarithms of the individual factors.

Corrections:

ln (a + b) does not equal ln(a) × ln(b), and there is no simple property that relates the logarithm of a sum to the logarithms of its addends.