Question

fill in the missing values to make the equations true.$log_{8}9 - log_{8}11 = log_{8}squareLXB0-2log_{7}3 = log_{7}square$

Explanation:

Step1: Apply log subtraction rule

Use $\log_b a - \log_b c = \log_b \frac{a}{c}$.
$\log_8 9 - \log_8 11 = \log_8 \frac{9}{11}$

Step2: Apply log addition rule

Use $\log_b a + \log_b c = \log_b (a \times c)$. Let the missing value be $x$:
$\log_5 x + \log_5 4 = \log_5 (4x) = \log_5 12$
Solve $4x=12$: $x=\frac{12}{4}=3$

Step3: Apply log power rule

Use $k\log_b a = \log_b a^k$.
$-2\log_7 3 = \log_7 3^{-2} = \log_7 \frac{1}{9}$

Answer:

1. $\frac{9}{11}$
2. $3$
3. $\frac{1}{9}$