Question - Solving and Combining Logarithmic Expressions
mathlogarithmic propertiessolving logarithmic expressionscombining logarithmic expressionssingle logarithm
Solution:
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).
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