Question

Math

Posted 4 months ago

```
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) $x=\frac{7}{2} \log _{6}(30)$
```

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Answer from Sia

Posted 4 months ago

Solution by Steps

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.

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