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Question: The value of \(81^{(1/\log_{5}3)} + 27^{\log_{9}36} + 3^{4/\log_{7} ⥂ 9}\) is equal to...

The value of 81(1/log⁡53)+27log⁡936+34/log⁡7⥂981^{(1/\log_{5}3)} + 27^{\log_{9}36} + 3^{4/\log_{7} ⥂ 9} is equal to

A

49

B

625

C

216

D

890

Answer

890

Explanation

Solution

81(1/log⁡53)+27log⁡936+34/log⁡7981^{(1/\log_{5}3)} + 27^{\log_{9}36} + 3^{4/\log_{7}9}

=34log⁡35+33.12log⁡336+34log⁡97= 3^{4\log_{3}5} + 3^{3.\frac{1}{2}\log_{3}36} + 3^{4\log_{9}7}

=3log⁡354+3log⁡3363/2+3log⁡374/2= 3^{\log_{3}5^{4}} + 3^{\log_{3}36^{3/2}} + 3^{\log_{3}7^{4/2}}

=54+363/2+72=890= 5^{4} + 36^{3/2} + 7^{2} = 890.