what is the value of log₂₇9?\n-3/2\n-2/3\n2/3\n3/2

Explanation:

Step1: Use change - of - base formula

Let $y = \log_{27}9$. By the change - of - base formula $\log_{a}b=\frac{\log_{c}b}{\log_{c}a}$, we can rewrite it as $y=\frac{\log 9}{\log 27}$.

Step2: Express numbers as powers of 3

Since $9 = 3^2$ and $27=3^3$, then $\log 9=\log(3^2) = 2\log 3$ and $\log 27=\log(3^3)=3\log 3$.

Step3: Substitute and simplify

$y=\frac{2\log 3}{3\log 3}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$