What is ln(2e^{-6})+(-2.268)*ln(0.15) ?

The solution to ln(2e^{-6})+(-2.268)*ln(0.15) is ln(0.36634…)

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simplify ln(2e^{-6})+(-2.268)*ln(0.15)

simplify

ln (2 e^{- 6}) + (- 2.268) \cdot ln (0.15)

ln (0.36634 \dots)

Decimal Notation

- 1.00418 \dots

Solution steps

ln (2 e^{- 6}) + (- 2.268) ln (0.15)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

(- 2.268) ln (0.15) = ln (0.1 5^{(- 2.268)})

= ln (2 e^{- 6}) + ln (0.1 5^{(- 2.268)})

Apply log rule:

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

ln (2 e^{- 6}) + ln (0.1 5^{(- 2.268)}) = ln (2 \cdot 0.1 5^{- 2.268} e^{- 6})

= ln (2 \cdot 0.1 5^{- 2.268} e^{- 6})

2 e^{- 6} \cdot 0.1 5^{(- 2.268)} = 0.36634 \dots

= ln (0.36634 \dots)

- ln (x + 1) + ln (x - 1) - 2 arctan (x)

lo g_{\frac{1}{2}} (\frac{1}{10})

lo g_{9} (5) e^{3} + lo g_{9} (7) e^{6}

- lo g_{10} (3.98 \cdot 1 0^{- 3})

ln (2 e^{t a n (x)})

What is ln(2e^{-6})+(-2.268)*ln(0.15) ?
The solution to ln(2e^{-6})+(-2.268)*ln(0.15) is ln(0.36634…)