Question

Using the change of base formula, the following expression was created:
log
2
128
log
2
32
. Identify the base of the original expression before the change of base formula was used.(1 point)
The base of the original expression was

Answer 1

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:

\[
\text{The base of the original expression was } 32.
\]