Certainly! Let’s solve the given equation step-by-step:
[tex]\[ \log_2 (\square) - \log_2 (3) = \log_2 \left( \frac{5}{3} \right) \][/tex]
### Step 1: Use the properties of logarithms
We know from the properties of logarithms that:
[tex]\[ \log_b (a) - \log_b (c) = \log_b \left( \frac{a}{c} \right) \][/tex]
Using this property, rewrite the left-hand side of the equation:
[tex]\[ \log_2 (\square) - \log_2 (3) = \log_2 \left( \frac{\square}{3} \right) \][/tex]
So, our equation now looks like:
[tex]\[ \log_2 \left( \frac{\square}{3} \right) = \log_2 \left( \frac{5}{3} \right) \][/tex]
### Step 2: Remove the logarithms
Since the bases of the logarithms are the same and the arguments are equal, we can equate the arguments directly:
[tex]\[ \frac{\square}{3} = \frac{5}{3} \][/tex]
### Step 3: Solve for the unknown
To isolate the unknown ([tex]\(\square\)[/tex]), we multiply both sides of the equation by 3:
[tex]\[ \square = \frac{5}{3} \times 3 \][/tex]
### Step 4: Simplify the result
[tex]\[ \square = 5 \][/tex]
Thus, the value that fits in the blank ([tex]\(\square\)[/tex]) is:
[tex]\[ \boxed{5} \][/tex]
