Let's solve the equation [tex]\(\log_2(x) - 3 = 1\)[/tex] step-by-step.
1. Isolate the logarithmic term:
To solve for [tex]\(x\)[/tex], we first need to isolate the term involving the logarithm.
[tex]\[
\log_2(x) - 3 = 1
\][/tex]
Add 3 to both sides of the equation:
[tex]\[
\log_2(x) - 3 + 3 = 1 + 3
\][/tex]
Simplifying this, we get:
[tex]\[
\log_2(x) = 4
\][/tex]
2. Exponentiate both sides to remove the logarithm:
The equation [tex]\(\log_2(x) = 4\)[/tex] means that [tex]\(x\)[/tex] is the number such that the base 2 logarithm of [tex]\(x\)[/tex] is 4. To find [tex]\(x\)[/tex], we need to rewrite the logarithmic equation in its exponential form:
[tex]\[
x = 2^4
\][/tex]
3. Calculate the value of [tex]\(x\)[/tex]:
Now, we calculate the exponent:
[tex]\[
x = 2^4 = 16
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{16}\)[/tex].
