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

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

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

simplify

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

- 4 ln (2)

Decimal Notation

- 2.77258 \dots

Solution steps

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

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

Add similar elements:

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

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

Apply log rule:

lo g_{a} (1) = 0

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

Simplify

lo g_{e} (4) : ln (4)

= 0 - 2 ln (4)

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

= - 2 ln (4)

Simplify

ln (4) : 2 ln (2)

= - 2 \cdot 2 ln (2)

Multiply the numbers:

2 \cdot 2 = 4

= - 4 ln (2)

lo g_{4} \frac{( x ^{2} \cdot \frac{1 ^{2}}{3 ^{2}} y ^{2} )}{x}

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

ln (\frac{0.18}{0.05})

ln (\frac{r ^{2} s ^{11}}{t ^{14}})

\frac{1}{3} lo g_{a} (\frac{2 x ^{2}}{b y ^{5}})

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