To find the value of [tex]\( x \)[/tex] in the equation [tex]\( \log_2(x) - 3 = 1 \)[/tex], follow these steps:
1. Isolate the logarithmic expression:
Start by adding 3 to both sides of the equation to isolate the [tex]\( \log_2(x) \)[/tex] term:
[tex]\[
\log_2(x) - 3 + 3 = 1 + 3
\][/tex]
Simplifying this, we get:
[tex]\[
\log_2(x) = 4
\][/tex]
2. Convert the logarithmic form to the exponential form:
Recall that the logarithmic equation [tex]\( \log_b(y) = z \)[/tex] is equivalent to the exponential equation [tex]\( b^z = y \)[/tex]. In this context, [tex]\( b = 2 \)[/tex], [tex]\( z = 4 \)[/tex], and [tex]\( y = x \)[/tex]. So:
[tex]\[
2^4 = x
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Calculate the value of [tex]\( 2^4 \)[/tex]:
[tex]\[
2^4 = 16
\][/tex]
Hence, the value of [tex]\( x \)[/tex] is 16.
Among the given choices:
- [tex]\( 2^1 = 2 \)[/tex]
- [tex]\( 2^2 = 4 \)[/tex]
- [tex]\( 2^3 = 8 \)[/tex]
- [tex]\( 2^4 = 16 \)[/tex]
Therefore, the correct answer is [tex]\( 2^4 \)[/tex], which is [tex]\( 16 \)[/tex].
