Question

Determine whether each statement is true or false. You have one submission for each statement. (a) ln(a+b)=ln(a) ln(b) for all a, b>0

A)True
B)False.

Answer 1

The statement is false; the correct property is that the logarithm of a product equals the sum of the logarithms ("ln(ab) = ln(a) + ln(b)"), not their addition.

Step-by-step explanation:

The statement ln(a+b) = ln(a) \u00d7 ln(b) for all a, b > 0 is false. According to the properties of logarithms, specifically exponents and their relation to logarithms, this statement does not hold true.

The correct property should be: the logarithm of a product of two numbers is the sum of the logarithms of the two numbers. Therefore, ln(ab) = ln(a) + ln(b), not the logarithm of their addition.

The logarithm of a quotient is expressed as the difference: ln(a/b) = ln(a) - ln(b). Therefore, we can see that logarithm rules for addition are different from those for multiplication and division.