log [ (√3)(2 - x)/(3x) ] = log (2 - x) - ¹/₂ log 3 - log x
Further explanation
Let's recall following formula about Exponents and Surds:
[tex]\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }[/tex]
[tex]\boxed { (a ^ b) ^ c = a ^ { b . c } } [/tex]
[tex]\boxed {a ^ b \div a ^ c = a ^ { b - c } }[/tex]
[tex]\boxed {\log a + \log b = \log (a \times b) }[/tex]
[tex]\boxed {\log a - \log b = \log (a \div b) }[/tex]
Let us tackle the problem!
[tex]\texttt{ }[/tex]
[tex]\log \frac{\sqrt{3}(2-x)}{(3x)} = \log \sqrt{3} + \log (2-x) - \log (3x)[/tex]
[tex]\log \frac{\sqrt{3}(2-x)}{(3x)} = \log 3^{1/2} + \log (2-x) - (\log 3 + \log x)[/tex]
[tex]\log \frac{\sqrt{3}(2-x)}{(3x)} = \frac{1}{2} \log 3 + \log (2-x) - \log 3 - \log x[/tex]
[tex]\log \frac{\sqrt{3}(2-x)}{(3x)} = \log (2-x) - \frac{1}{2}\log 3 - \log x[/tex]
[tex]\texttt{ }[/tex]
Learn more
- Coefficient of A Square Root : https://brainly.com/question/11337634
- The Order of Operations : https://brainly.com/question/10821615
- Write 100,000 Using Exponents : https://brainly.com/question/2032116
Answer details
Grade: High School
Subject: Mathematics
Chapter: Exponents and Surds
Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.
