Question

pls give answers with steps ​

Answer 1

Answer:

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[tex]

3x+y=81

⇒3x+y=34

or x+y=4                 ...(i)

Also (81)x−y=3

⇒34(x−y)=31,

4x−4y=1            ...(ii)

Solving equations (i) and (ii), we get

x178 and y=158

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

1) 3^(x + y) = 81 ⇒3^(x+ y) = ( 3 )^4 (∵ " ^ " this symbol means " to the power of " )

⇒x + y = 4 --------eq ( 1 ) ( say ) ( ∵Bases are equal, then powers should be equal )

81^(x - y) = 3 ⇒ [(3)^4]^(x - y) = 3

⇒( 3 )^(4x - 4y) = 3 ⇒4x - 4y = 1---eq (2) (∵Bases are equal,powers should be equal )

Now multiply eq ( 1 ) with 4 , we get

4 × ( x + y = 4 ) ⇒4x +:4y = 16---eq ( 3 )

Now adding eq ( 2 ) + eq ( 3 ),we get

4x - 4y + 4x + 4y = 1 + 16

8x = 17 ⇒ x = 17/8

On substituting x = 17/8 in eq ( 1 ),we have

17/8 + y = 4

y = 4 - 17/8 = 32- 17/8 = 15/8

∴ x = 17/8 and y = 15/8 is the answer.

2) ( - 2 )^(x + 1 ) × ( - 2 )^(5) = ( - 2 )^7 (∵" ^ " this symbol means " to the power of " )

⇒ ( - 2 ) ^ (x + 1 + 5 ) = ( - 2 ) ^7 ( ∵ Bases are equal, then powers should be add )

⇒ ( - 2 )^(x + 6 ) = ( - 2 )^7

⇒ x + 6 = 7 (∵ Bases are equal then powers should be equal )

⇒ x = 7 - 6

⇒ x = 1 is the answer.