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Sagot :
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].
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].
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