Problem
$$
2 \cdot 3^{\frac{2 x}{7}}=30
$$

Which of the following is the solution of the equation?
Choose 1 answer:
(A) $x=\frac{7}{2} \log _{30}(6)$
(B) $x=\frac{7}{2} \log _{15}(3)$
(C) $x=\frac{7}{2} \log _{3}(15)$
(D) $x=\frac{7}{2} \log _{6}(30)$

Question

Problem
$$
2 \cdot 3^{\frac{2 x}{7}}=30
$$

Which of the following is the solution of the equation?
Choose 1 answer:
(A) $x=\frac{7}{2} \log _{30}(6)$
(B) $x=\frac{7}{2} \log _{15}(3)$
(C) $x=\frac{7}{2} \log _{3}(15)$
(D) $x=\frac{7}{2} \log _{6}(30)$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Start with the given equation: $2 \cdot 3^{\frac{2x}{7}} = 30$ ‖ ‖ step 2 ⋮ Divide both sides by 2 to isolate the exponential term: $3^{\frac{2x}{7}} = 15$ ‖ ‖ step 3 ⋮ Apply the logarithm to both sides of the equation: $\frac{2x}{7} \log(3) = \log(15)$ ‖ ‖ step 4 ⋮ Solve for x: $x = \frac{7}{2} \frac{\log(15)}{\log(3)}$ ‖ ‖ step 5 ⋮ Simplify the expression for x using the properties of logarithms: $x = \frac{7}{2} \log_{3}(15)$ ‖ ***C*** ∻Key Concept∻ ⚹Logarithmic form of an exponential equation⚹ ∻Explanation∻ ⚹To solve an exponential equation, take the logarithm of both sides and then isolate the variable.◊What is the value of $x$ in the equation $2 \cdot 3^{\frac{2x}{7}}=30$?⍭ Generate me a similar question◊⚹

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