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Popular >

simplify ln((x^2-3x)/(x^2))

Solution

simplify

ln (\frac{x ^{2} - 3 x}{x ^{2}})

Solution

ln (x^{2} - 3 x) - 2 ln (x)

Solution steps

ln (\frac{x ^{2} - 3 x}{x ^{2}})

Apply log rule:

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

ln (\frac{x ^{2} - 3 x}{x ^{2}}) = ln (x^{2} - 3 x) - ln (x^{2})

= ln (x^{2} - 3 x) - ln (x^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (x^{2} - 3 x) - 2 ln (x)

Popular Examples

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simplify ln^2(x)+ln(x)+1 simplify

ln^{2} (x) + ln (x) + 1

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lo g_{10} (\frac{x}{3 y})

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- lo g_{10} (\frac{1 \cdot 1 0 ^{- 14}}{1.3 \cdot 1 0 ^{- 3}})

expand ln((1-sqrt(3)i)^{10})expand

ln ((1 - 3 i)^{10})

Frequently Asked Questions (FAQ)

What is ln((x^2-3x)/(x^2)) ?
The solution to ln((x^2-3x)/(x^2)) is ln(x^2-3x)-2ln(x)