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Find the value of A that makes the following equation true for all values of x. 0.9^(60 x)=A^(x) Choose 1 answer: (A) A=0.9*60 (B) A=0.9^(60) (c) A=(60)/(0.9) (D) A=60^(0.9)

Find the value of A A that makes the following equation true for all values of x x .\newline0.960x=Ax 0.9^{60 x}=A^{x} \newlineChoose 11 answer:\newline(A) A=0.9⋅60 A=0.9 \cdot 60 \newline(B) A=0.960 A=0.9^{60} \newline(C) A=600.9 A=\frac{60}{0.9} \newline(D) A=600.9 A=60^{0.9}

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Q. Find the value of A A that makes the following equation true for all values of x x .\newline0.960x=Ax 0.9^{60 x}=A^{x} \newlineChoose 11 answer:\newline(A) A=0.9⋅60 A=0.9 \cdot 60 \newline(B) A=0.960 A=0.9^{60} \newline(C) A=600.9 A=\frac{60}{0.9} \newline(D) A=600.9 A=60^{0.9}
  1. Understand and Identify Bases: Understand the equation and identify the bases.\newlineWe are given the equation 0.960x=Ax0.9^{60x} = A^{x}. We need to find the value of AA such that this equation holds true for all xx. To do this, we need to compare the bases of the exponents.
  2. Isolate Bases and Exponents: Isolate the bases and their exponents. Since the exponents are already isolated (60x60x on the left side and xx on the right side), we can equate the bases to solve for AA.
  3. Equate the Bases: Equate the bases.\newlineSince the exponents are multiples of each other, we can equate the bases as follows:\newline0.960=A0.9^{60} = A
  4. Solve for A: Solve for A.\newlineTo find AA, we simply take the 6060th power of 0.90.9:\newlineA=0.960A = 0.9^{60}
  5. Match the Solution: Match the solution to the given choices.\newlineWe have found that A=0.960A = 0.9^{60}, which matches choice (B)(B).

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