Certainly! Let's solve the equation [tex]\(\log_2(x) - 3 = 1\)[/tex] step-by-step to find the value of [tex]\(x\)[/tex].
1. Start with the given equation:
[tex]\[
\log_2(x) - 3 = 1
\][/tex]
2. Isolate the logarithmic term:
Add 3 to both sides of the equation to isolate [tex]\(\log_2(x)\)[/tex]:
[tex]\[
\log_2(x) = 1 + 3
\][/tex]
3. Simplify the right-hand side:
Perform the addition:
[tex]\[
\log_2(x) = 4
\][/tex]
4. Rewrite the logarithmic equation in exponential form:
Recall that if [tex]\(\log_b(a) = c\)[/tex], then [tex]\(a = b^c\)[/tex]. Here, [tex]\(b = 2\)[/tex], [tex]\(a = x\)[/tex], and [tex]\(c = 4\)[/tex]:
[tex]\[
x = 2^4
\][/tex]
5. Calculate the exponent:
Compute [tex]\(2^4\)[/tex]:
[tex]\[
2^4 = 16
\][/tex]
So, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\log_2(x) - 3 = 1\)[/tex] is:
[tex]\[
x = 16
\][/tex]
