Question

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

$\log 4+\log 25$

Short answer

On simplifying the expression we get,

$2$

Step-by-step solution

Step 1. Given information 

We are given an expression,

$\log 4+\log 25$

Use the logarithm properties to condense the given expression.

Step 2. Identify the logarithm property  

Use product rule of logarithm,

${\log }_{a}M+{\log }_{a}N={\log }_a(M·N)$

Step 3. Simplifying the expression 

Using the product rule of logarithm, we get

$$\begin{gathered} \log 4+\log 25={\log }_{10}(4·25) \\ \log 4+\log 25={\log }_{10}100 \\ \log 4+\log 25={\log }_{10}{10}^2 \end{gathered}$$

Using ${\log }_a{a}^b=b$, we get

$\log 4+\log 25=2$