Question

What is the equation written as a single Logarithm

Answer 1

Answer:

Choice 3

$log \frac{x^2y}{z^2}$

Step-by-step explanation:

We use 3 of the rules of logarithms

• Product Rule :          

              $\log (ab) = \log a + \log b$

• Quotient Rule:  

               $\log\frac{a}{b} = \log a - \log b$      

• Power Rule

               $\log (a^n) = n\log a$

$\log\frac{x^2y}{z^2} =\ log(x^2y) - \log(z^2)$     (quotient rule)

$\log(x^2y) = \log x^2 + \log y$           (product rule)

$\log x^2 = 2\log x$                         (power rule)

$\log z^2 = 2\log z$                            (power rule)

Final result

$log \frac{x^2y}{z^2} = 2\log x + \log y - \log z$