Condense the logarithmic expression:
\(\ln 5 - \ln a + 6 \ln b - 6 \ln c\)
Answer (2)
U se : l n x − l n y = l n ( y x ) l n x + l n y = l n ( x ⋅ y ) l n x y = y ⋅ l n x
0;\ b > 0\ and\ c > 0"> l n 5 − l na + 6 l nb − 6 l n c = l n a 5 + l n b 6 − l n c 6 = l n a 5 + l n c 6 b 6 = l n a c 6 5 b 6 w h ere : a > 0 ; b > 0 an d c > 0
To condense the expression ln 5 − ln a + 6 ln b − 6 ln c , use logarithm properties to rewrite it as ln ( a c 6 5 b 6 ) . This involves properties of differences and products of logarithms. The final condensed form is ln ( a c 6 5 b 6 ) .
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