Question

Which of the following are true (log here denotes the logarithm base 10)?

I. log(a) + log(b) = log(a + b)
II. log(2) = 2 log(x)

Answer 1

I. log(a) + log(b) = log(a + b) is not true. II. log(2) = 2 log(x) is true.

Step-by-step explanation:

The first statement (I) is not true. According to the property of logarithms, the sum of the logarithms of two numbers is equal to the logarithm of their product, not the logarithm of their sum. So, the correct statement would be log(a) + log(b) = log(ab).

The second statement (II) is true. The logarithm of a number raised to a power is equal to the product of the exponent and the logarithm of the number. So, log(2) = log(x^2) = 2log(x).