which of the following shows the true solution to the logarithmic equation $3\\log_2(2x)=3$?\n$x = - 1$\n$x…

Explanation:

Step1: Simplify the equation

Divide both sides of $3\log_{2}(2x)=3$ by 3. We get $\log_{2}(2x) = 1$.

Step2: Convert to exponential form

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

Step3: Solve for x

Since $2 = 2x$, dividing both sides by 2 gives $x = 1$. Also, for the logarithm $\log_{2}(2x)$ to be well - defined, the argument $2x>0$. When $x=-1$, $2x=-2<0$ and when $x = 0$, $2x=0$. So $x=-1$ and $x = 0$ are not in the domain of the original logarithmic function.

Answer:

$x = 1$