What is simplify-log_{10}(2.3*10^{-9}) ?

The solution to simplify-log_{10}(2.3*10^{-9}) is -log_{10}(2.3)+9

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simplify-log_{10}(2.3*10^{-9})

simplify

- lo g_{10} (2.3 \cdot 1 0^{- 9})

- lo g_{10} (2.3) + 9

Decimal Notation

8.63827 \dots

Solution steps

- lo g_{10} (2.3 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (2.3 \cdot 1 0^{- 9}) = lo g_{10} (2.3) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (2.3) + lo g_{10} (1 0^{- 9}))

Apply log rule:

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

lo g_{10} (1 0^{- 9}) = - 9 lo g_{10} (10)

= - (lo g_{10} (2.3) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (2.3) - 9)

Distribute parentheses

= - (lo g_{10} (2.3)) - (- 9)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (2.3) + 9

ln (\frac{1}{2 ^{n}} \cdot e^{- 2 x} e^{- 3 t})

\frac{3}{2} (lo g_{10} (4.94145) - lo g_{10} (761.21))

ln (\frac{r \cdot 0.04}{2.51})

3 lo g_{5} (a) - 3 lo g_{5} (b)

\frac{1}{2} ln (a) + 2 ln (c)

What is simplify-log_{10}(2.3*10^{-9}) ?
The solution to simplify-log_{10}(2.3*10^{-9}) is -log_{10}(2.3)+9