Answer :

To solve
[tex]$$
\log_2\frac{12}{25},
$$[/tex]
we can follow these steps:

1. First, evaluate the fraction:
[tex]$$
\frac{12}{25} = 0.48.
$$[/tex]

2. Next, recall the change-of-base formula for logarithms:
[tex]$$
\log_2(0.48) = \frac{\ln(0.48)}{\ln(2)}.
$$[/tex]

3. After carrying out the calculation, the value is found to be approximately:
[tex]$$
\log_2(0.48) \approx -1.0588936890535685.
$$[/tex]

Thus, the final answer is
[tex]$$
\log_2\frac{12}{25} \approx -1.0588936890535685.
$$[/tex]