Question

What is the true solution to the logarithmic equation below? log Subscript 4 Baseline left-bracket log Subscript 4 Baseline (2 x) right-bracket = 1
x = 2
x = 8
x = 64
x = 128

Answer 1

Answer:

x = 128

Step-by-step explanation:

The given logarithm is

$log_{4}(log_{4}(2x))=1$

To find the value of $x$, we need to uses some logarithm and exponent properties.

First, we have

$log_{a}M=b \implies a^{b}=M$

Applying this property, we have

$log_{4}(log_{4}(2x))=1\\4^{1}= log_{4}(2x)$

Then, we use the property again

$4^{4}=2x$

Now, we solve for $x$

$x=\frac{256}{2}\\ x=128$

Therefore, the right answer is the last choice: x = 128.

Answer 2

Step-by-step explanation:

$log_4(log_4 2x)=1 \\ \\ \therefore \: log_4 2x = {4}^{1} \\ \\ \therefore \: log_4 2x =4 \\ \\ \therefore \: 2x = {4}^{4} \\ \\ \therefore \: 2x = 256 \\ \\ \therefore \: x = \frac{256}{2} \\ \\ \therefore \: x = 128$