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Find the value of 
A that makes the following equation true for all values of 
x.

2^(x)=A^((x)/( 12))
Choose 1 answer:
(A) 
A=2*12
(B) 
A=2^((1)/(12))
(C) 
A=2^(12)
(D) 
A=((1)/(12))^(2)

Find the value of AA that makes the following equation true for all values of xx. \newline2x=A(x12)2^{x}=A^{\left(\frac{x}{12}\right)} \newlineChoose 11 answer: \newline(A) A=2×12A=2\times 12 \newline(B) A=2(112)A=2^{\left(\frac{1}{12}\right)} \newline(C) A=212A=2^{12} \newline(D) A=(112)2A=\left(\frac{1}{12}\right)^{2}

Full solution

Q. Find the value of AA that makes the following equation true for all values of xx. \newline2x=A(x12)2^{x}=A^{\left(\frac{x}{12}\right)} \newlineChoose 11 answer: \newline(A) A=2×12A=2\times 12 \newline(B) A=2(112)A=2^{\left(\frac{1}{12}\right)} \newline(C) A=212A=2^{12} \newline(D) A=(112)2A=\left(\frac{1}{12}\right)^{2}
  1. Simplify Equation: Simplify the equation to find AA:2x=A(x12)2^{x} = A^{\left(\frac{x}{12}\right)}To make the equation true for all xx, the bases and exponents on both sides must be equal.
  2. Set Exponents Equal: Set the exponents equal to each other:\newlineSince the bases are different, equate the exponents:\newlinex=x12x = \frac{x}{12}\newlineThis step is incorrect because it does not help in solving for AA. We need to equate the bases instead.

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