High School

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Which of the following is equivalent to the equation below?

\[ \log_2 128 = x \]

Select one:

A. \( 2^x = 128 \)

B. \( x^2 = 128 \)

C. \( 2x = 128 \)

D. \( x = 2^{128} \)

Answer :

Answer: [tex]2^x=128[/tex]

Step-by-step explanation:

Recall that [tex]\log_b a=c[/tex] can be rewritten as [tex]b^c=a[/tex].

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Rewritten by : Barada

The equivalent of the equation log₂128 = x is a. 2ˣ = 128.

We need to understand that log₂128 = x means the power to which 2 must be raised to get 128. Rewriting this, we get 2ˣ = 128. Therefore, the correct answer is:

  • a. 2ˣ = 128

Let's verify:

  1. 128 in decimal form is 2⁷, so log₂128 = x can be written as x = 7.

  2. Therefore, 2ˣ = 128 correctly translates log₂128 = x to exponential form.