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Answer :
We start with the equation
$$
2^x = 128.
$$
Recall the definition of logarithms: if
$$
a^b = c,
$$
then this is equivalent to
$$
\log_a(c) = b.
$$
In our case, we have $a = 2$, $b = x$, and $c = 128$. Applying the definition yields
$$
\log_2(128) = x.
$$
Thus, the exponential equation rewritten in logarithmic form is
$$
\log_2(128) = x.
$$
We can also verify this by recognizing that $128 = 2^7$, so
$$
\log_2(128) = \log_2(2^7) = 7,
$$
which tells us that $x = 7$.
Among the given choices, the correct logarithmic equation is the one that matches
$$
\log_2(128) = x.
$$
$$
2^x = 128.
$$
Recall the definition of logarithms: if
$$
a^b = c,
$$
then this is equivalent to
$$
\log_a(c) = b.
$$
In our case, we have $a = 2$, $b = x$, and $c = 128$. Applying the definition yields
$$
\log_2(128) = x.
$$
Thus, the exponential equation rewritten in logarithmic form is
$$
\log_2(128) = x.
$$
We can also verify this by recognizing that $128 = 2^7$, so
$$
\log_2(128) = \log_2(2^7) = 7,
$$
which tells us that $x = 7$.
Among the given choices, the correct logarithmic equation is the one that matches
$$
\log_2(128) = x.
$$
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