To find the value of [tex]\( x \)[/tex] in the equation [tex]\( \log_2 8 = x \)[/tex], we need to understand that the logarithm [tex]\(\log_2 8\)[/tex] asks the question: "To what exponent must we raise 2 to get 8?"
Here are the detailed steps to solve this equation:
1. Express the logarithmic equation in its exponential form:
[tex]\[
\log_2 8 = x \quad \text{is equivalent to} \quad 2^x = 8
\][/tex]
2. Recognize that [tex]\( 8 \)[/tex] can be written as a power of [tex]\( 2 \)[/tex]:
[tex]\[
8 \quad \text{can be expressed as} \quad 2^3
\][/tex]
Therefore,
[tex]\[
2^x = 2^3
\][/tex]
3. Compare the exponents on both sides of the equation:
Since the bases are the same (both are 2), the exponents must be equal. This gives us:
[tex]\[
x = 3
\][/tex]
4. Conclusion:
[tex]\[
\log_2 8 = x \implies x = 3
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 3 \)[/tex].
