Answered

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85. If [tex][tex]$2^{3x}=8$[/tex][/tex], then what must be the value of [tex][tex]$x$[/tex][/tex]?

A) 1
B) 2
C) 4
D) 8

Sagot :

GinnyAnswer
To solve the equation [tex]\(2^{3x} = 8\)[/tex], we'll proceed with the following steps:

1. Express the number 8 as a power of 2:
Observe that [tex]\(8\)[/tex] can be written as [tex]\(2^3\)[/tex]. Therefore, we have:
[tex]\[ 2^{3x} = 2^3 \][/tex]

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

3. Solve for [tex]\(x\)[/tex]:
Divide both sides of the equation by 3:
[tex]\[ x = \frac{3}{3} = 1 \][/tex]

Thus, the value of [tex]\(x\)[/tex] is:

[tex]\[ \boxed{1} \][/tex]
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