1.

7log base2 (16/15)+5logbase 2 (25/24)

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Answer:

GIVEN,

→ 7 log_{2}( \frac{16}{15} ) + 5 log_{2}( \frac{25}{24} )

= log_{2}(( { \frac{16}{15}) }^{7} ) + log_{2}(( { \frac{25}{24}) }^{5} )

= log_{2}( ( { \frac{16}{15} )}^{7} \times ( ({ \frac{25}{24}) }^{5} )

= log_{2}( \frac{{2}^{28} \times {5}^{10} }{ {2}^{15} \times {<klux>3</klux>}^{12} \times {5}^{7} } )

= log_{2}( \frac{ {2}^{13} \times {5}^{3} }{ {3}^{12} } )

= 13 log_{2}(2) + 3 log_{2}(5) - 12 log_{2}(3)

= 13 + 3 log_{2}(5) - 12 log_{2}(3)

FORMULAE used:-

1) LOG(ab) = log(a) + log(B)

2) log(a/b) = log(a) - log(b)

3) log(a^(m)) = mlog(a)



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