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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Cancel the common factor:

x

= ln^{2} (\frac{1}{x ^{2}})

Simplify

ln (\frac{1}{x ^{2}}) : - ln (x^{2})

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

Apply exponent rule:

(- a)^{n} = a^{n},

if

n

is even

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

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

Popular Examples

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- lo g_{10} (3.52 x 1 0^{- 4})

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x + ln (3.9 i)

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lo g_{7} (\frac{15}{x})

simplify-3ln(3)+2ln(4)simplify

- 3 ln (3) + 2 ln (4)

Frequently Asked Questions (FAQ)

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