Logarithms Practice Test 2

Question : 37 of 39

Marks: +1, -0

25^{(1/2+\log_{1/5}27+\log_125 81)} = ?

Solution:

25^{(1/2+\log_{1/5}27+\log_ {125} 81)}

= 5^{2(1/2+\log_{ 5^{-1}}3^3+\log_ {5^3}3^4)}

= 5^{ (1+2×(-3)\log_{5}3+2×4/3\log_5 3)}

= 5^{ (\log_5 5+ \log_{5}3^{-6}+ \log_5 3^{8/3})}

=5^{\log _5 ({5×3^{8/3}}/3^6)}

={5×3^{2/3}}/3^4

= {5 √^3 9}/ 81

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