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Popular >

simplify 2ln(x)-ln^2(x)

Solution

simplify

2 ln (x) - ln^{2} (x)

Solution

ln (x)

Solution steps

2 ln (x) - ln^{2} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (x) = ln (x^{2})

= ln (x^{2}) - ln^{2} (x)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{2}) - ln^{2} (x) = ln (\frac{x ^{2}}{x})

= ln (\frac{x ^{2}}{x})

Cancel the common factor:

x

= ln (x)

Popular Examples

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5 lo g_{10} (x) - 2 lo g_{10} (x + 1)

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lo g_{10} (x) + lo g_{10} (5) - lo g_{10} (3)

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ln (3) - ln (\frac{1}{2})

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Frequently Asked Questions (FAQ)

What is 2ln(x)-ln^2(x) ?
The solution to 2ln(x)-ln^2(x) is ln(x)