If $$ \log _{2}(3 x+6)=3 $$, then $$ x=\square $$ You may enter the exact value or round to 4 decimal places.

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We are given
$$
\log_{2}(3x+6)=3.
$$
By the definition of the logarithm, this implies:
$$
3x+6=2^3.
$$
Calculating $$2^3$$, we have:
$$
3x+6=8.
$$
Subtracting 6 from both sides gives:
$$
3x=2.
$$
Finally, dividing both sides by 3, we find:
$$
x=\frac{2}{3}.
$$
$$ x = \frac{2}{3} $$

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

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