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Sagot :
Answer:
[tex]2a - b -c[/tex]
Step-by-step explanation: We know that:
[tex]log_{2} 5 = a\\log_{2} 3 = b\\log_2 7 = c\\[/tex]
and we want:
[tex]log_2 \frac{25}{21}[/tex].
We can form the numerator using just the first fact (since 5^2 is 25) and the denominator using the latter two (since 3*7 = 21).
[tex]log_2 \frac{25}{21} = log_2 \frac{5^2}{3*7}.[/tex]
The logarithm of a division can be expanded by subtracting the numerator and denominator (while still keeping the log). The logarithm of a product can be expanded by adding the terms while keeping the log. If the logarithm is raised to a power, we can bring it down as a factor:
[tex]log_2 \frac{5^2}{3*7} = log_2(5)^2 - log_2 (3*7) = 2 log_2(5) - (log_2 3 + log_2 7)[/tex]
[tex]= 2 log_2(5) - log_2 3 - log_2 7[/tex] .
Substituting the variables:
[tex]2 log_2(5) - log_2 3 - log_2 7 = 2a - b - c[/tex]
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