Chapter 4.4, Problem 1E

The logarithm of a product of two numbers is the same as the __________ of the logarithms of these numbers. So log₅(25 · 125) = __________ + __________.

To determine

To find: The logarithm of a product of two numbers is same as the __________ of the logarithms of these numbers. So ${\log }_5(25.125)=$ _____+ _____.

Answer to Problem 1E

The logarithm of a product of two numbers is same as the sum of the logarithms of these numbers. So ${\log }_5(25.125)=$ ${\log }_5\left(25\right)$+ ${\log }_5\left(125\right)$.

Explanation of Solution

Recall that ${\log }_a\left(AB\right)={\log }_{a}A+{\log }_{a}B$.

By above result, the logarithm of a product of two numbers is same as the sum of the logarithms of these numbers.

Thus, the product ${\log }_5(25\cdot 125)$ can be expressed as ${\log }_5\left(25\right)+{\log }_5\left(125\right)$.