What is simplify-log_{10}(6.9*10^{-9}) ?

The solution to simplify-log_{10}(6.9*10^{-9}) is -log_{10}(6.9)+9

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simplify-log_{10}(6.9*10^{-9})

simplify

- lo g_{10} (6.9 \cdot 1 0^{- 9})

- lo g_{10} (6.9) + 9

Decimal Notation

8.16115 \dots

Solution steps

- lo g_{10} (6.9 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (6.9 \cdot 1 0^{- 9}) = lo g_{10} (6.9) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (6.9) + 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} (6.9) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (6.9) - 9)

Distribute parentheses

= - (lo g_{10} (6.9)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (6.9) + 9

ln (q) - ln (s)

ln (1000) - ln (9)

7 \cdot ln (- \frac{1}{2} ln (81))

2 - 3 ln (- 2) - 4 + 3 ln (- 4)

ln (\frac{n ^{2}}{n + 1})

What is simplify-log_{10}(6.9*10^{-9}) ?
The solution to simplify-log_{10}(6.9*10^{-9}) is -log_{10}(6.9)+9