Answer :
To solve the equation [tex]\(2^{3x} = 8\)[/tex], we will follow these steps:
1. Rewrite 8 as a power of 2:
We know that [tex]\(8 = 2^3\)[/tex]. So, we can rewrite the equation as:
[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]:
To find [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] must be [tex]\(1\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
So the value of [tex]\(x\)[/tex] is [tex]\(\boxed{1}\)[/tex].
1. Rewrite 8 as a power of 2:
We know that [tex]\(8 = 2^3\)[/tex]. So, we can rewrite the equation as:
[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]:
To find [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] must be [tex]\(1\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
So the value of [tex]\(x\)[/tex] is [tex]\(\boxed{1}\)[/tex].
