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marshall27 [118]
3 years ago
9

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
Mathematics
2 answers:
Alborosie3 years ago
8 0

Answer:

<h2>x = 128</h2>

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.

Luda [366]3 years ago
6 0

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

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