What is log_{10}(1.8*10^{-5}) ?

The solution to log_{10}(1.8*10^{-5}) is log_{10}(18)-6

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simplify log_{10}(1.8*10^{-5})

simplify

lo g_{10} (1.8 \cdot 1 0^{- 5})

lo g_{10} (18) - 6

Decimal Notation

- 4.74472 \dots

Solution steps

lo g_{10} (1.8 \cdot 1 0^{- 5})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (1.8 \cdot 1 0^{- 5}) = lo g_{10} (1.8) + lo g_{10} (1 0^{- 5})

= lo g_{10} (1.8) + lo g_{10} (1 0^{- 5})

lo g_{10} (1.8) = lo g_{10} (18) - 1

= (lo g_{10} (18) - 1) + lo g_{10} (1 0^{- 5})

Apply log rule:

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

lo g_{10} (1 0^{- 5}) = - 5

= (lo g_{10} (18) - 1) - 5

(lo g_{10} (18) - 1) - 5 = lo g_{10} (18) - 6

= lo g_{10} (18) - 6

\frac{9}{2} \cdot \frac{1}{2}

(2 + 1)^{3}

427 - 6 \frac{1}{3}

\frac{5}{2 \frac{1}{6}}

- 12 - (- 11)

What is log_{10}(1.8*10^{-5}) ?
The solution to log_{10}(1.8*10^{-5}) is log_{10}(18)-6