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What is the value of A when we rewrite 3^(x) as A^(5x) ? Choose 1 answer: (A) A=3 (B) A=3^(-5) (c) A=3^((1)/(5)) (D) A=3^(-(1)/(5))

What is the value of A A when we rewrite 3x 3^{x} as A5x A^{5 x} ?\newlineChoose 11 answer:\newline(A) A=3 A=3 \newline(B) A=3−5 A=3^{-5} \newline(C) A=315 A=3^{\frac{1}{5}} \newline(D) A=3−15 A=3^{-\frac{1}{5}}

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Full solution

Q. What is the value of A A when we rewrite 3x 3^{x} as A5x A^{5 x} ?\newlineChoose 11 answer:\newline(A) A=3 A=3 \newline(B) A=3−5 A=3^{-5} \newline(C) A=315 A=3^{\frac{1}{5}} \newline(D) A=3−15 A=3^{-\frac{1}{5}}
  1. Given equation: We are given the equation 3x3^{x} and we want to express it in the form A5xA^{5x}. To do this, we need to find a value for AA such that raising AA to the power of 5x5x will give us the same result as raising 33 to the power of xx.
  2. Equating the expressions: We can start by equating the two expressions:\newline3x=A5x3^{x} = A^{5x}\newlineSince the bases must be the same for the exponents to be equal, we can deduce that A5A^5 must be equal to 33.
  3. Finding A: To find AA, we take the fifth root of both sides of the equation A5=3A^5 = 3: \newlineA=(3)(1/5)A = (3)^{(1/5)}\newlineThis simplifies to AA being the fifth root of 33.
  4. Checking the answer choices: Now we can check the answer choices to see which one matches our result:\newline(A) A=3A=3 (This would imply A5=35A^5 = 3^5, which is not correct.)\newline(B) A=3−5A=3^{-5} (This would imply A5=(3−5)5=3−25A^5 = (3^{-5})^5 = 3^{-25}, which is not correct.)\newline(C) A=315A=3^{\frac{1}{5}} (This matches our result, so it is correct.)\newline(D) A=3−15A=3^{-\frac{1}{5}} (This would imply A5=(3−15)5=3−1A^5 = (3^{-\frac{1}{5}})^5 = 3^{-1}, which is not correct.)

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