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Sagot :
To solve the equation [tex]\(\log(2x) = 2\)[/tex], follow these steps:
1. Understand that [tex]\(\log\)[/tex] without a base explicitly given typically refers to [tex]\(\log_{10}\)[/tex], the common logarithm. So we rephrase the given equation as:
[tex]\[ \log_{10}(2x) = 2 \][/tex]
2. Rewrite the logarithmic equation in its exponential form. Recall that [tex]\(a = \log_{b}(c)\)[/tex] can be rewritten as [tex]\(b^a = c\)[/tex]. Applying this principle here:
[tex]\[ 10^2 = 2x \][/tex]
3. Calculate [tex]\(10^2\)[/tex]:
[tex]\[ 10^2 = 100 \][/tex]
4. Solve for [tex]\(x\)[/tex] by isolating it on one side of the equation:
[tex]\[ 2x = 100 \][/tex]
[tex]\[ x = \frac{100}{2} \][/tex]
5. Simplify the fraction:
[tex]\[ x = 50 \][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\log(2x) = 2\)[/tex] is [tex]\(\boxed{50}\)[/tex].
1. Understand that [tex]\(\log\)[/tex] without a base explicitly given typically refers to [tex]\(\log_{10}\)[/tex], the common logarithm. So we rephrase the given equation as:
[tex]\[ \log_{10}(2x) = 2 \][/tex]
2. Rewrite the logarithmic equation in its exponential form. Recall that [tex]\(a = \log_{b}(c)\)[/tex] can be rewritten as [tex]\(b^a = c\)[/tex]. Applying this principle here:
[tex]\[ 10^2 = 2x \][/tex]
3. Calculate [tex]\(10^2\)[/tex]:
[tex]\[ 10^2 = 100 \][/tex]
4. Solve for [tex]\(x\)[/tex] by isolating it on one side of the equation:
[tex]\[ 2x = 100 \][/tex]
[tex]\[ x = \frac{100}{2} \][/tex]
5. Simplify the fraction:
[tex]\[ x = 50 \][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(\log(2x) = 2\)[/tex] is [tex]\(\boxed{50}\)[/tex].
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