solve: log₂(3x + 1) = 4\na $\frac{17}{3}$\nb 5\nc $\frac{7}{3}$\nd 9

Explanation:

Step1: Convert to exponential form

By the definition of logarithms, if $\log_{a}b = c$, then $a^{c}=b$. So, if $\log_{2}(3x + 1)=4$, we have $2^{4}=3x + 1$. $$2^{4}=3x + 1$$

Step2: Calculate the power

Calculate $2^{4}=16$. So the equation becomes $16 = 3x+1$. $$16=3x + 1$$

Step3: Solve for x

Subtract 1 from both sides: $16-1=3x$, which simplifies to $15 = 3x$. Then divide both sides by 3: $x=\frac{15}{3}=5$. $$x = 5$$

Answer:

B. 5