$[-/7$ Points$]$

SCALCET$914\mathrm{.}1\mathrm{.}081.$

$($a$)$ Show that, by taking logarithms, the general Cobb$-$Douglas function $P=b{L}^a{K}^{1-a}$ can be expressed as

$ln(\frac{p}{K})=ln(b)$ aln$(\frac{L}{K})$

$P=b{L}^a{K}^{1-a}=>\frac{p}{K}=(,)L^a{K}^{-a}$

$\frac{p}{K}=(,)(\frac{L}{K}{)}^a$

$ln(\frac{p}{K})=ln((,)(\frac{L}{K}{)}^a)$

$ln(\frac{p}{K})=ln(b)$ aln$(\frac{L}{K})$