Step-by-step explanation:
[tex]log_4(log_4 2x)=1 \\ \\ \therefore \: log_4 2x = {4}^{1} \\ \\ \therefore \: log_4 2x =4 \\ \\ \therefore \: 2x = {4}^{4} \\ \\ \therefore \: 2x = 256 \\ \\ \therefore \: x = \frac{256}{2} \\ \\ \therefore \: x = 128[/tex]
Answer:
Step-by-step explanation:
The given logarithm is
[tex]log_{4}(log_{4}(2x))=1[/tex]
To find the value of [tex]x[/tex], we need to uses some logarithm and exponent properties.
First, we have
[tex]log_{a}M=b \implies a^{b}=M[/tex]
Applying this property, we have
[tex]log_{4}(log_{4}(2x))=1\\4^{1}= log_{4}(2x)[/tex]
Then, we use the property again
[tex]4^{4}=2x[/tex]
Now, we solve for [tex]x[/tex]
[tex]x=\frac{256}{2}\\ x=128[/tex]
Therefore, the right answer is the last choice: x = 128.
