What is log_{10}(3.2*e^{-5}) ?

The solution to log_{10}(3.2*e^{-5}) is log_{10}(3.2)-5log_{10}(e)

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simplify log_{10}(3.2*e^{-5})

simplify

lo g_{10} (3.2 \cdot e^{- 5})

lo g_{10} (3.2) - 5 lo g_{10} (e)

Decimal Notation

- 1.66632 \dots

Solution steps

lo g_{10} (3.2 e^{- 5})

Apply log rule:

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

lo g_{10} (3.2 e^{- 5}) = lo g_{10} (3.2) + lo g_{10} (e^{- 5})

= lo g_{10} (3.2) + lo g_{10} (e^{- 5})

Apply log rule:

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

lo g_{10} (e^{- 5}) = - 5 lo g_{10} (e)

= lo g_{10} (3.2) - 5 lo g_{10} (e)

ln (14) - \frac{2}{3} ln (3 x) - \frac{4}{3} ln (4 - 3 x)

lo g_{10} (\frac{2 x ^{2}}{y})

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

3 lo g_{b} (x) + lo g_{b} (y)

182000 (ln (0.45) - ln (1.3))

What is log_{10}(3.2*e^{-5}) ?
The solution to log_{10}(3.2*e^{-5}) is log_{10}(3.2)-5log_{10}(e)