Answer
$\log\left({\frac{2}{3}}\right)$
Work Step by Step
Use the Power Property of Logarithms to rewrite this expression. The property states that $\log_b {m^n} = n \log_b {m}$. Thus, the given expression is equivalent to:
$\log {8} - \log {6^{2}} + \log {3}$
Evaluate the exponential term:
$\log {8} - \log {36} + \log {3}$
Use the Quotient Property of Logarithms. According to this property, $\log_b {m} - \log_b {n} = \log_b \frac {m}{n}$. Thus, the expression above is equivalent to:
$\log\left(\frac{8}{36}\right) + \log {3}$
Use the Product Property of Logarithms. According to this property, $\log_b {mn} = \log_b {m} + \log_b {n}$. Thus, the expression above is equivalent to:
$\log{\left[\left(\frac{8}{36}\right)(3)\right]}$
Multiply to simplify:
$\log{\left(\frac{8 \cdot 3}{36}\right)}$
Simplify:
$\log{\frac{24}{36}}$
Simplify the fraction by dividing both numerator and denominator by their greatest common factor, $12$:
$\log{\left(\frac{2}{3}\right)}$
