To solve the equation [tex]\(\log z + 12 = 9\)[/tex], let's follow these steps:
1. Rearrange the equation:
[tex]\[
\log z + 12 = 9
\][/tex]
Subtract 12 from both sides to isolate the logarithmic term:
[tex]\[
\log z = 9 - 12
\][/tex]
Simplify the right-hand side:
[tex]\[
\log z = -3
\][/tex]
2. Convert the logarithmic equation to its exponential form:
The equation [tex]\(\log z = -3\)[/tex] can be rewritten in its exponential form as:
[tex]\[
z = 10^{-3}
\][/tex]
3. Calculate the numerical value:
[tex]\[
10^{-3} = 0.001
\][/tex]
Therefore, [tex]\(z = 0.001\)[/tex].
The correct answer is:
[tex]\[
\boxed{0.001}
\][/tex]
