Question

As you can see I keep getting questions wrong.... Can you answer the last question?

Answer 1

Answer:

  y = 0

Step-by-step explanation:

It is always a good idea to look at the question and make some observations about it. Here, you might observe ...

• all of the bases are powers of 3: 243 = 3^5; 9 = 3^2
• y is a factor of every exponent

The latter observation is important, because it means that when y=0, every exponential expression has a value of 1. Hence y = 0 is a solution.

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To solve the equation, you can write it in terms of powers of 3.

  (3^5)^(-y) = (3^-5)^(3y)·(3^2)^(-2y)

  3^(-5y) = 3^(-15y)·3^(-4y)

  3^(-5y) = 3^(-19y)

  -5y = -19y . . . . . . . . equating exponents; equivalent to taking log base 3

  14y = 0 . . . . . . . . . . add 19y

  y = 0 . . . . . . . . . . . one solution

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The rules of exponents we used are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

  1/a^b = a^-b