Sure! Let's solve the problem step-by-step.
Given the equation [tex]\(5x + 2 = 3\)[/tex], we need to isolate [tex]\(x\)[/tex] to find its value.
1. Start by subtracting 2 from both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
5x + 2 - 2 = 3 - 2
\][/tex]
Simplifying this gives:
[tex]\[
5x = 1
\][/tex]
2. Next, divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{1}{5}
\][/tex]
Therefore:
[tex]\[
x = 0.2
\][/tex]
3. Now that we know [tex]\(x = 0.2\)[/tex], we need to find [tex]\(\log x\)[/tex], which is the natural logarithm (base [tex]\(e\)[/tex]) of [tex]\(x\)[/tex]. Substituting the value:
[tex]\[
\log(0.2)
\][/tex]
4. Evaluating the natural logarithm, we get:
[tex]\[
\log(0.2) \approx -1.6094379124341003
\][/tex]
So, the value of [tex]\(\log x\)[/tex] is approximately [tex]\(-1.6094379124341003\)[/tex].
