What is log_{e}(9/10) ?

The solution to log_{e}(9/10) is 2ln(3)-ln(10)

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simplify log_{e}(9/10)

simplify

lo g_{e} (\frac{9}{10})

2 ln (3) - ln (10)

Decimal Notation

- 0.10536 \dots

Solution steps

lo g_{e} (\frac{9}{10})

Apply log rule:

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

lo g_{e} (\frac{9}{10}) = lo g_{e} (9) - lo g_{e} (10)

= lo g_{e} (9) - lo g_{e} (10)

Apply log rule:

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

= ln (9) - lo g_{e} (10)

Apply log rule:

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

= ln (9) - ln (10)

ln (9) = 2 ln (3)

= 2 ln (3) - ln (10)

2 (lo g_{m} (x) - 5 lo g_{m} (y)) + 2 lo g_{m} (z)

lo g_{10} (0.98 \cdot 111.2 \cdot 1 0^{- 6} \cdot 2 π \cdot 200.27)

- \frac{8.5}{30} ln (\frac{1}{2})

3 lo g_{10} (6 - x) - lo g_{10} (72 - x^{3})

lo g_{10} (\frac{23.16}{2})