To find the value of [tex]\( x \)[/tex] given the equation [tex]\( 4x = \log_2 64 \)[/tex]:
1. First, we need to determine the value of [tex]\( \log_2 64 \)[/tex].
- By definition, [tex]\( \log_2 64 \)[/tex] represents the power to which the base 2 must be raised to obtain 64.
- We can rewrite 64 as [tex]\( 2^6 \)[/tex] since [tex]\( 2^6 = 64 \)[/tex].
- Therefore, [tex]\( \log_2 64 = 6 \)[/tex].
2. Now that we know [tex]\( \log_2 64 = 6 \)[/tex], we can substitute this value back into the equation [tex]\( 4x = \log_2 64 \)[/tex].
[tex]\[
4x = 6
\][/tex]
3. To solve for [tex]\( x \)[/tex], we divide both sides of the equation by 4:
[tex]\[
x = \frac{6}{4}
\][/tex]
4. Simplifying the fraction, we get:
[tex]\[
x = 1.5
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 1.5 \)[/tex]. Given this, the correct value from the provided options should ideally be compared, but it seems there is no direct matching choice here. However, based on the calculated value, [tex]\( x \)[/tex] is not approximately close to 32 or 16, implying a continuation or part of another contextual problem not included in the visible question.
