Solve the equation. $$ \begin{array}{c}2 \log _{10}(3 x)=4 \ x=[?]\end{array} $$

Question

UpStudy AI · Accepted Answer

To solve the equation:

$$
2 \log_{10}(3x) = 4
$$

Follow these steps:

1. **Isolate the logarithm:**

Divide both sides of the equation by 2:

$$
   \log_{10}(3x) = \frac{4}{2} \implies \log_{10}(3x) = 2
   $$

2. **Convert the logarithmic equation to its exponential form:**

Recall that $$\log_{10}(A) = B$$ is equivalent to $$10^B = A$$. Applying this:

$$
   3x = 10^2 \implies 3x = 100
   $$

3. **Solve for $$x$$:**

$$
   x = \frac{100}{3} \approx 33.\overline{3}
   $$

**Final Answer:**  
$$x = \dfrac{100}{3}$$
$$ x = \dfrac{100}{3} $$

Solve the equation. \[ \begin{array}{c}2 \log _{10}(3 x)=4 \\ x=[?]\end{array} \]