Question

How would you write the following expression as a sum or difference? `"log"(root(3)(2 - x)/(3x))`

Answer 1

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:

$\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }$

$\boxed { (a ^ b) ^ c = a ^ { b . c } }$

$\boxed {a ^ b \div a ^ c = a ^ { b - c } }$

$\boxed {\log a + \log b = \log (a \times b) }$

$\boxed {\log a - \log b = \log (a \div b) }$

Let us tackle the problem!

$\texttt{ }$

$\log \frac{\sqrt{3}(2-x)}{(3x)} = \log \sqrt{3} + \log (2-x) - \log (3x)$

$\log \frac{\sqrt{3}(2-x)}{(3x)} = \log 3^{1/2} + \log (2-x) - (\log 3 + \log x)$

$\log \frac{\sqrt{3}(2-x)}{(3x)} = \frac{1}{2} \log 3 + \log (2-x) - \log 3 - \log x$

$\log \frac{\sqrt{3}(2-x)}{(3x)} = \log (2-x) - \frac{1}{2}\log 3 - \log x$

$\texttt{ }$

Learn more

• Coefficient of A Square Root : brainly.com/question/11337634
• The Order of Operations : brainly.com/question/10821615
• Write 100,000 Using Exponents : 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.