What is simplify-log_{10}(6.37*10^{-9}) ?

The solution to simplify-log_{10}(6.37*10^{-9}) is -log_{10}(6.37)+9

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simplify-log_{10}(6.37*10^{-9})

simplify

- lo g_{10} (6.37 \cdot 1 0^{- 9})

- lo g_{10} (6.37) + 9

Decimal Notation

8.19586 \dots

Solution steps

- lo g_{10} (6.37 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (6.37 \cdot 1 0^{- 9}) = lo g_{10} (6.37) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (6.37) + 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} (6.37) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (6.37) - 9)

Distribute parentheses

= - (lo g_{10} (6.37)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (6.37) + 9

- \frac{2 ln ( 2 )}{- 2 ln ( 2 ) - 1}

- lo g_{10} (1.83 \cdot 1 0^{- 6})

2 (lo g_{6} (x) - 2 lo g_{6} (z)) + 3 lo g_{6} (w)

ln (\frac{x + 1}{9 - x ^{2}})

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

What is simplify-log_{10}(6.37*10^{-9}) ?
The solution to simplify-log_{10}(6.37*10^{-9}) is -log_{10}(6.37)+9