Question

use properties of logarithms to condense the logarithmic expression. write the expression as a single logarithm whose coefficient is 1. where possible, evaluate logarithmic expressions.
log 2 + log 5
log 2 + log 5 = \square (simplify your answer.)

Explanation:

Step1: Recall log addition property

The property of logarithms states that $\log_a M + \log_a N = \log_a (M \times N)$ (for the same base \(a\), here base is 10, so we can use this property). So for $\log 2 + \log 5$, we apply this property: $\log (2\times5)$.

Step2: Simplify the product inside log

Calculate \(2\times5 = 10\), so the expression becomes $\log 10$.

Step3: Evaluate $\log 10$

We know that for base 10 logarithm, $\log_{10} 10 = 1$ (since $10^1 = 10$).

Answer:

1