Answered

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If [tex][tex]$2^{2x} = 2^3$[/tex][/tex], what is the value of [tex][tex]$x$[/tex][/tex]?

A. [tex]\frac{2}{3}[/tex]
B. [tex]\frac{3}{2}[/tex]
C. 2
D. 3

Sagot :

GinnyAnswer
To solve the equation [tex]\(2^{2x} = 2^3\)[/tex], we can use the property of exponents that states if the bases are the same, we can set the exponents equal to each other. Here's a step-by-step solution:

1. Given Equation:
[tex]\[ 2^{2x} = 2^3 \][/tex]

2. Set the Exponents Equal:
Since the bases (2) are the same, we can set the exponents equal to each other:
[tex]\[ 2x = 3 \][/tex]

3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], divide both sides of the equation by 2:
[tex]\[ x = \frac{3}{2} \][/tex]

Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\frac{3}{2}\)[/tex].

Among the given choices:

[tex]\[ \boxed{\frac{3}{2}} \][/tex]
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