What is log_{10}(1.2e^{-3}) ?

The solution to log_{10}(1.2e^{-3}) is log_{10}(1.2)-3log_{10}(e)

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simplify log_{10}(1.2e^{-3})

simplify

lo g_{10} (1.2 e^{- 3})

lo g_{10} (1.2) - 3 lo g_{10} (e)

Decimal Notation

- 1.22370 \dots

Solution steps

lo g_{10} (1.2 e^{- 3})

Apply log rule:

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

lo g_{10} (1.2 e^{- 3}) = lo g_{10} (1.2) + lo g_{10} (e^{- 3})

= lo g_{10} (1.2) + lo g_{10} (e^{- 3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (e^{- 3}) = - 3 lo g_{10} (e)

= lo g_{10} (1.2) - 3 lo g_{10} (e)

ln (A e^{\frac{3}{2} t^{2}})

ln ∣ 4 ∣ + 2 ln (4^{2} + 4) - ln ∣ 1 ∣ + 2 ln (1^{2} + 4)

ln (w) + 6 ln (u) - 2 ln (v)

\frac{9}{2} ln (\frac{3}{2}) + \frac{3}{8} - ln (2) - ln (2)

What is log_{10}(1.2e^{-3}) ?
The solution to log_{10}(1.2e^{-3}) is log_{10}(1.2)-3log_{10}(e)