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To evaluate the given logarithm, we can rewrite it as an exponential equation by using the definition of a logarithm.
$g_{b}(x)=y⇔x=b_{y} $
The above means that the logarithm $y$ is the exponent to which $b$ must be raised to get $x.$ For our exercise, $y$ is the exponent to which $2$ must be raised to get $1281 .$
$g_{2}(1281 )=y⇔1281 =2_{y} $
Therefore, we should rewrite $1281 $ into a power of $2$ and the resulting exponent will be our answer.
Thus, $g_{2}(1281 )=-7$.

$1281 $

$a1 =a_{-1}$

$128_{-1}$

WritePowWrite as a power

$(2_{7})_{-1}$

PowPow$(a_{m})_{n}=a_{m⋅n}$

$2_{-7}$