To combine the given logarithmic expressions into a single logarithm using the properties of logarithms, we can use the following rules:
- \( k \log_b(x) = \log_b(x^k) \) for any constant \( k \).
- \( \log_b(x) + \log_b(y) = \log_b(xy) \).
- \( \log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right) \).
Now, let's analyze the expression \( 13\log_2 a - \frac{1}{4}\log_2 b + 2\log_2 c \).
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Rewrite each part using the first property:
- \( 13\log_2 a = \log_2(a^{13}) \)
- \( -\frac{1}{4}\log_2 b = \log_2(b^{-\frac{1}{4}}) \)
- \( 2\log_2 c = \log_2(c^2) \)
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Combine all parts using the addition and subtraction properties: \[ \log_2(a^{13}) + \log_2(c^2) + \log_2(b^{-\frac{1}{4}}) = \log_2\left(\frac{a^{13} c^2}{b^{\frac{1}{4}}}\right) \]
Thus, the expression \( 13\log_2 a - \frac{1}{4}\log_2 b + 2\log_2 c \) can be rewritten as a single logarithm: \[ \log_2\left(\frac{a^{13} c^2}{b^{\frac{1}{4}}}\right) \]
The other expressions can also be analyzed similarly, but the first one is clearly able to be converted into a single logarithmic form utilizing the properties applied above.
Therefore, the answer is: The expression that can be rewritten as a single logarithm is \( 13\log_2 a - \frac{1}{4}\log_2 b + 2\log_2 c \).