Solving and Combining Logarithmic Expressions
To solve the expression given, 2 log 5 + 5 log x, and express it as a single logarithm, we will utilize the properties of logarithms:
1. The power rule: log(a^b) = b * log(a)
2. The product rule: log(a) + log(b) = log(a * b)
Let's apply these rules step by step:
The first term 2 log 5 can be rewritten using the power rule as:
log(5^2) = log(25)
The second term 5 log x can be rewritten using the power rule as:
log(x^5)
Now, adding the two log terms using the product rule:
log(25) + log(x^5) = log(25 * x^5)
Now the expression is written as a single logarithm: log(25 * x^5)
Looking at the answer choices, the correct answer is B. log(25 * x^5).
