6.4: Homework Score: $$ 14.5 / 16 $$ Answered: $$ 15 / 16 $$ Question 16 If $$ \log _{2}(3 x+3)=2 $$, then $$ x=\square $$ Question Help: D Video

Question

UpStudy AI · Accepted Answer

To solve the equation $$ \log_{2}(3x + 3) = 2 $$, we can rewrite it in exponential form. The equation states that $$ 3x + 3 $$ is equal to $$ 2^2 $$.

1. Rewrite the logarithmic equation in exponential form:
   $$
   3x + 3 = 2^2
   $$

2. Calculate $$ 2^2 $$:
   $$
   2^2 = 4
   $$
   So, we have:
   $$
   3x + 3 = 4
   $$

3. Now, isolate $$ 3x $$ by subtracting 3 from both sides:
   $$
   3x = 4 - 3
   $$
   $$
   3x = 1
   $$

4. Finally, divide both sides by 3 to solve for $$ x $$:
   $$
   x = \frac{1}{3}
   $$

Thus, the solution is:
$$
x = \frac{1}{3}
$$
$$ x = \frac{1}{3} $$

6.4: Homework
Score: Answered:
Question 16
If , then Question Help: D Video