To determine the value of [tex]\( x \)[/tex] in the equation [tex]\(\log_2(x) - 3 = 1\)[/tex], follow these step-by-step instructions:
1. Start with the given equation:
[tex]\[
\log_2(x) - 3 = 1
\][/tex]
2. Isolate [tex]\(\log_2(x)\)[/tex] by adding 3 to both sides of the equation:
[tex]\[
\log_2(x) - 3 + 3 = 1 + 3
\][/tex]
[tex]\[
\log_2(x) = 4
\][/tex]
3. Rewrite the logarithmic equation in its exponential form. Remember that [tex]\(\log_2(x) = 4\)[/tex] can be rewritten as:
[tex]\[
2^4 = x
\][/tex]
4. Calculate the exponent:
[tex]\[
2^4 = 16
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 16 \)[/tex]. Among the given options:
- [tex]\(2^3 = 8\)[/tex]
- [tex]\(2^1 = 2\)[/tex]
- [tex]\(2^4 = 16\)[/tex]
- [tex]\(2^2 = 4\)[/tex]
The correct answer is:
[tex]\[
2^4
\][/tex]
