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3*2^((x)/(5))=150 Which of the following is the solution of the equation? Choose 1 answer: (A) x=log_(50)(2) (B) x=5log_(50)(2) (C) x=5log_(2)(50) (D) x=log_(2)(50)

3⋅2x5=150 3 \cdot 2^{\frac{x}{5}}=150 \newlineWhich of the following is the solution of the equation?\newlineChoose 11 answer:\newline(A) x=log⁡50(2) x=\log _{50}(2) \newline(B) x=5log⁡50(2) x=5 \log _{50}(2) \newline(C) x=5log⁡2(50) x=5 \log _{2}(50) \newline(D) x=log⁡2(50) x=\log _{2}(50)

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Full solution

Q. 3⋅2x5=150 3 \cdot 2^{\frac{x}{5}}=150 \newlineWhich of the following is the solution of the equation?\newlineChoose 11 answer:\newline(A) x=log⁡50(2) x=\log _{50}(2) \newline(B) x=5log⁡50(2) x=5 \log _{50}(2) \newline(C) x=5log⁡2(50) x=5 \log _{2}(50) \newline(D) x=log⁡2(50) x=\log _{2}(50)
  1. Divide by 33: Divide both sides of the equation by 33 to isolate the term with the exponent on one side.\newline3×2x/5=1503 \times 2^{x/5} = 150\newline(3×2x/5)/3=150/3(3 \times 2^{x/5}) / 3 = 150 / 3\newline2x/5=502^{x/5} = 50
  2. Take logarithm: Take the logarithm with base 22 of both sides to solve for xx.
    log⁡2(2x/5)=log⁡2(50)\log_2(2^{x/5}) = \log_2(50)
    Using the property of logarithms that log⁡b(bx)=x\log_b(b^x) = x, we get:
    x5=log⁡2(50)\frac{x}{5} = \log_2(50)
  3. Multiply by 55: Multiply both sides of the equation by 55 to solve for xx.(x5)×5=log⁡2(50)×5\left(\frac{x}{5}\right) \times 5 = \log_2(50) \times 5x=5×log⁡2(50)x = 5 \times \log_2(50)

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