What is simplify-2log_{e}(1/4) ?

The solution to simplify-2log_{e}(1/4) is 4ln(2)

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simplify-2log_{e}(1/4)

simplify

- 2 lo g_{e} (\frac{1}{4})

4 ln (2)

Decimal Notation

2.77258 \dots

Solution steps

- 2 lo g_{e} (\frac{1}{4})

Apply log rule:

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

lo g_{e} (\frac{1}{4}) = lo g_{e} (1) - lo g_{e} (4)

= - 2 (lo g_{e} (1) - lo g_{e} (4))

Apply log rule:

lo g_{a} (1) = 0

= - 2 (- lo g_{e} (4) + 0)

Apply log rule:

lo g_{e} (x) = ln (x)

= - 2 (- ln (4) + 0)

0 - ln (4) = - ln (4)

= - 2 (- ln (4))

Apply rule

- (- a) = a

= 2 ln (4)

Simplify

ln (4) : 2 ln (2)

= 2 \cdot 2 ln (2)

Multiply the numbers:

2 \cdot 2 = 4

= 4 ln (2)

ln (\frac{3}{1})

ln (2 X)

ln (4 (e^{3 x})^{\frac{1}{6}})

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

ln (\frac{0.2}{12})

What is simplify-2log_{e}(1/4) ?
The solution to simplify-2log_{e}(1/4) is 4ln(2)