To identify the base of the original expression before the change of base formula was used, we start with the expression:
\[ \frac{\log_2 128}{\log_2 32} \]
According to the change of base formula, this expression can also be written as:
\[ \log_b a = \frac{\log_k a}{\log_k b} \]
where \( b \) is the base of the logarithm we want to find, \( a \) is the argument (128), and \( k \) is any positive base we choose (in this case, 2).
In the expression \(\frac{\log_2 128}{\log_2 32}\), if we set:
- \( a = 128 \)
- \( b = 32 \)
Then we can apply the change of base formula as follows:
\[ \log_{32} 128 = \frac{\log_2 128}{\log_2 32} \]
From this, we can conclude that the base of the original expression (prior to using the change of base formula) is:
\[ \text{The base of the original expression was } 32. \]
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