If $$ \log _{2}(3 x+2)=2 $$, then $$ x=\square $$ You may enter the exact value or round to 4 decimal places.

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UpStudy AI · Accepted Answer

1. Start with the given equation:
   $$
   \log_{2}(3x + 2) = 2
   $$

2. Rewrite the logarithmic equation in exponential form. Recall that if $$\log_{a}(b) = c$$, then $$a^c = b$$. Here, $$a = 2$$, $$b = 3x + 2$$, and $$c = 2$$. Thus, we have:
   $$
   2^2 = 3x + 2
   $$

3. Calculate $$2^2$$:
   $$
   4 = 3x + 2
   $$

4. Solve for $$x$$ by first subtracting 2 from both sides:
   $$
   4 - 2 = 3x
   $$
   Simplifying:
   $$
   2 = 3x
   $$

5. Finally, divide both sides by 3 to isolate $$x$$:
   $$
   x = \frac{2}{3}
   $$

Thus, the solution is:
$$
x = \frac{2}{3}
$$
$$ x = \frac{2}{3} $$

If , then
You may enter the exact value or round to 4 decimal places.

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If , then You may enter the exact value or round to 4 decimal places.