AMC 10 Daily Practice - Exponent

Complete problem set with solutions and individual problem pages

Problem 2 Medium

Given that {{2}^{x}}={{4}^{y+1}} and {{27}^{y}}={{3}^{x-1}}. Find the value of x-y.

  • A.

    1

  • B.

    2

  • C.

    3

  • D.

    4

  • E.

    5

Answer:C
Solution

∵ {{2}^{x}}={{4}^{y+1}},

∴ {{2}^{x}}={{2}^{2y+2}},

∴ x=2y+2①.

∵ {{27}^{y}}={{3}^{x-1}},

∴ {{3}^{3y}}={{3}^{x-1}},

∴ 3y=x-1②.

Solve the system of equations ① and ②: \begin{cases}x=4 \\ y=1 \\ \end{cases}, we get x-y=3.

Related Problems
Problem 1 AMC 10 Daily Practice - Exponent
Problem 3 AMC 10 Daily Practice - Exponent
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