What is log_{e}(4)-log_{e}(2)-log_{e}(3) ?

The solution to log_{e}(4)-log_{e}(2)-log_{e}(3) is ln(2/3)

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simplify log_{e}(4)-log_{e}(2)-log_{e}(3)

simplify

lo g_{e} (4) - lo g_{e} (2) - lo g_{e} (3)

ln (\frac{2}{3})

Decimal Notation

- 0.40546 \dots

Solution steps

lo g_{e} (4) - lo g_{e} (2) - lo g_{e} (3)

Rewrite

- lo g_{e} (2) - lo g_{e} (3)

- (lo g_{e} (2) + lo g_{e} (3))

= lo g_{e} (4) - (lo g_{e} (2) + lo g_{e} (3))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{e} (2) + lo g_{e} (3) = lo g_{e} (2 \cdot 3)

= lo g_{e} (4) - lo g_{e} (2 \cdot 3)

Multiply the numbers:

2 \cdot 3 = 6

= lo g_{e} (4) - lo g_{e} (6)

Apply log rule:

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

lo g_{e} (4) - lo g_{e} (6) = lo g_{e} (\frac{4}{6})

= lo g_{e} (\frac{4}{6})

Cancel the common factor:

2

= lo g_{e} (\frac{2}{3})

Apply log rule:

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

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

ln (13) - ln (12)

2.12 - \frac{0.0592}{2} \cdot lo g_{10} (\frac{0.4}{0.6})

3 lo g_{10} (a) - 4 lo g_{10} (y)

4 ln (\frac{y}{x}) + 4 ln (x)

ln (y = x \cdot e^{x^{2}} \cdot (x^{2} + 10)^{10})

What is log_{e}(4)-log_{e}(2)-log_{e}(3) ?
The solution to log_{e}(4)-log_{e}(2)-log_{e}(3) is ln(2/3)