To solve the equation [tex]\(\log(x) = 2\)[/tex] for [tex]\(x\)[/tex], follow these steps:
1. Understand the Equation: Recognize that the equation [tex]\(\log(x) = 2\)[/tex] is in logarithmic form. In this expression, the logarithm is assumed to be base 10 (common logarithm), so it is actually [tex]\(\log_{10}(x) = 2\)[/tex].
2. Convert to Exponential Form: To solve for [tex]\(x\)[/tex], you need to convert the logarithmic equation to its equivalent exponential form. The general relationship between logarithms and exponents is:
[tex]\[
\log_{b}(a) = c \quad \text{is equivalent to} \quad a = b^c
\][/tex]
Here, [tex]\(b\)[/tex] is the base of the logarithm, [tex]\(a\)[/tex] is the argument of the logarithm, and [tex]\(c\)[/tex] is the result.
Applying this to our equation, [tex]\(\log_{10}(x) = 2\)[/tex], we get:
[tex]\[
x = 10^2
\][/tex]
3. Calculate the Exponential: Now, compute [tex]\(10^2\)[/tex].
[tex]\[
10^2 = 10 \times 10 = 100
\][/tex]
Hence, the value of [tex]\(x\)[/tex] is:
[tex]\[
x = 100
\][/tex]
So, the exact answer is:
[tex]\[
x = 100
\][/tex]
