How do you evaluate 2 log_3 12 - 2 log_3 4?

May 5, 2016

I found: $2$

Explanation:

I would use the properties of logs and write:

${\log}_{3} {\left(12\right)}^{\textcolor{red}{2}} - {\log}_{3} {\left(4\right)}^{\textcolor{red}{2}} =$

and then:

$= {\log}_{3} {\left(\frac{12}{4}\right)}^{2} = {\log}_{3} \left({3}^{2}\right) = 2$
The text passage contains a mathematical question involving logarithms and provides a step-by-step solution leading to an answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
How do you evaluate 2 log_3 12 - 2 log_3 4?

May 5, 2016

I found: $2$

Explanation:

I would use the properties of logs and write:

${\log}_{3} {\left(12\right)}^{\textcolor{red}{2}} - {\log}_{3} {\left(4\right)}^{\textcolor{red}{2}} =$

and then:

$= {\log}_{3} {\left(\frac{12}{4}\right)}^{2} = {\log}_{3} \left({3}^{2}\right) = 2$
user
The text passage contains a mathematical question involving logarithms and provides a step-by-step solution leading to an answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER