Question

Simplify it :
$log(16 \times \sqrt[3]{256} ) - log(6 \div \sqrt[4]{448} )$
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Answer 1

log (16×256⅓)-log(6/448¼)

= log ( 4²×(4⁴)⅓) - log (6/2⁶×7)

=log (4^(2+4/3) ) - log (6/2⁶×7)

= log (4^(10/3)) - log (6/2⁶×7)

$= log( {4}^{ \frac{10}{3} } ) - log( \frac{6}{ {2}^{6 } \times 7 } ) \\ = log( \frac{ {4}^{ \frac{10}{3} \times {2}^{6 } } \times 7}{6} ) \\ = log( \frac{ {2}^{ \frac{20}{3} \times {2 }^{6} } \times 7}{6} ) \\ = log( \frac{ {2}^{ \frac{38}{3} } \times 7 }{3 \times 2} ) \\ = log( \frac{ {2}^{ \frac{35}{3} } \times 7}{3} )$