Question

find the value of the following ​

Answer 1

Answer:

log ( a base b ) = 1/log ( b base a )

use this concept here ,

[ 81 ^{1/log (9 base 5 )} + 3^{3/log ( 3 base√6 ) } ]/409.[ (√7)^{2/log(7 base 25)} - (125)^{log ( 6 base 25) }

solution :-

81^{1/log(9 base 5)

= (9²)^{log( 5 base 9)

= 9^{ log5² base 9 )

= 25

3^{ 3/log(3 base √6 )

=3^{3log( √6 base 3) }

=3^{ log(√6³ base 3)

=√6³

=6√6

(√7)^{ 2/log(7 base 25) }

=(√7)^{2log(25 base 7)

=(7)^{2×1/2log(25 base 7)}

=(7)^{log(25 base 7) }

=25

(125)^{log( 6 base 25 )

=(5³)^{log ( 6 base 5² )

=(5)^{3/2log( 6 base 5)

= (6)^3/2

=6√6

now,

put all calculated value in question ,

=(25 + 6√6)(25 -6√6)/409

=(625 -216)/409

=409/409

= 1

hence , answer is 1

hope you got ur answe

Step-by-step explanation:

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