What is simplify-log_{10}(3.6*10^{-9}) ?

The solution to simplify-log_{10}(3.6*10^{-9}) is -log_{10}(3.6)+9

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simplify-log_{10}(3.6*10^{-9})

simplify

- lo g_{10} (3.6 \cdot 1 0^{- 9})

- lo g_{10} (3.6) + 9

Decimal Notation

8.44369 \dots

Solution steps

- lo g_{10} (3.6 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (3.6 \cdot 1 0^{- 9}) = lo g_{10} (3.6) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (3.6) + 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} (3.6) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (3.6) - 9)

Distribute parentheses

= - (lo g_{10} (3.6)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (3.6) + 9

ln (\frac{x}{5 + x})

ln (20000000) - ln (300000)

2 ln (4) - ln (6) + 3 ln (2)

- lo g_{10} (2.09 (1 0^{- 12}))

- 20 lo g_{e} (\frac{3}{5})

What is simplify-log_{10}(3.6*10^{-9}) ?
The solution to simplify-log_{10}(3.6*10^{-9}) is -log_{10}(3.6)+9