Use the properties of logarithms to evaluate $\log _ { 27 } 9 + \log _ { 27 } 81$ without a calculator.
A)2
B) $ \frac{2}{3} $
C) $ \frac{3}{4} $
D) 4
E)1

Question

Quizplus · Accepted Answer

The properties of logarithms allow us to simplify the expression. First, recognize that 9 = 27^(2/3) and 81 = 27^(4/3). Therefore, $\log _ { 27 } 9 = \frac{2}{3}$ and $\log _ { 27 } 81 = \frac{4}{3}$. Adding these together gives $\frac{2}{3} + \frac{4}{3} = 2$.

Use the Properties of Logarithms to Evaluate log⁡279+log⁡2781\log _ { 27 } 9 + \log _ { 27 } 81log27​9+log27​81

Use the Properties of Logarithms to Evaluate $\log _ { 27 } 9 + \log _ { 27 } 81$