Answer :
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]
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]
