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Popular >

simplify log_{e}(1/(a^2))

Solution

simplify

lo g_{e} (\frac{1}{a ^{2}})

Solution

- 2 ln (a)

Solution steps

lo g_{e} (\frac{1}{a ^{2}})

Apply log rule:

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

lo g_{e} (\frac{1}{a ^{2}}) = lo g_{e} (1) - lo g_{e} (a^{2})

= lo g_{e} (1) - lo g_{e} (a^{2})

Apply log rule:

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

lo g_{e} (a^{2}) = 2 lo g_{e} (a)

= lo g_{e} (1) - 2 lo g_{e} (a)

Apply log rule:

lo g_{a} (1) = 0

= 0 - 2 lo g_{e} (a)

Simplify

lo g_{e} (a) : ln (a)

= 0 - 2 ln (a)

0 - 2 ln (a) = - 2 ln (a)

= - 2 ln (a)

Popular Examples

join-(5ln(5/12))/3 join

- \frac{5 ln ( \frac{5}{12} )}{3}

simplify ln(100/1)simplify

ln (\frac{100}{1})

simplify ln((18)/(9.42))simplify

ln (\frac{18}{9.42})

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

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

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

Frequently Asked Questions (FAQ)

What is log_{e}(1/(a^2)) ?
The solution to log_{e}(1/(a^2)) is -2ln(a)