Let a = 3 2 and b = 5 1/6 6 1 . If x , y ∈ R are such that 3 x + 2 y = lo g a ( 18 ) 4 5 2 x − y = lo g b ( 1080 ) and then 4 x + 5 y is equal to . ________.

Question

Let a = 3 2 ​ and b = 5 1/6 6 ​ 1 ​ . If x , y ∈ R are such that 3 x + 2 y = lo g a ​ ( 18 ) 4 5 ​ 2 x − y = lo g b ​ ( 1080 ​ ) ​ and then 4 x + 5 y is equal to . ________.

TestHub · Accepted Answer

​ 3 x + 2 y = lo g 3 2 ​ ​ ( 3 2 ​ ) 2 5 ​ = 2 5 ​ ⇒ 6 x + 4 y = 5 …… ( 1 ) ​ 2 x − y = lo g 5 1/6 6 ​ 1 ​ ​ ( 5 6 1 ​ 6 ​ ) 3 = − 3 ⇒ ⇒ ​ 2 x − y = − 3 ..... ( 2 ) equation (1) − ( 2 ) 4 x + 5 y = 8 ​

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