what is the true solution to the logarithmic equation below?\nlog₄log₄(2x) = 1\no x = 2\no x = 8\no x =…

Explanation:

Step1: Use log - property

If $\log_{a}b = c$, then $b=a^{c}$. For $\log_{4}[\log_{4}(2x)] = 1$, we have $\log_{4}(2x)=4^{1}=4$.

Step2: Apply log - property again

Since $\log_{4}(2x) = 4$, then $2x=4^{4}$.

Step3: Solve for x

$4^{4}=256$, so $2x = 256$, and $x=\frac{256}{2}=128$.

Answer:

$x = 128$