What is simplify-log_{10}(8*10^{-9}) ?

The solution to simplify-log_{10}(8*10^{-9}) is -3log_{10}(2)+9

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simplify-log_{10}(8*10^{-9})

simplify

- lo g_{10} (8 \cdot 1 0^{- 9})

- 3 lo g_{10} (2) + 9

Decimal Notation

8.09691 \dots

Solution steps

- lo g_{10} (8 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (8 \cdot 1 0^{- 9}) = lo g_{10} (8) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (8) + 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} (8) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (8) - 9)

lo g_{10} (8) = 3 lo g_{10} (2)

= - (3 lo g_{10} (2) - 9)

Distribute parentheses

= - (3 lo g_{10} (2)) - (- 9)

Apply minus-plus rules

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

= - 3 lo g_{10} (2) + 9

lo g_{2} ((\frac{b}{c})^{2})

- lo g_{10} (1.9 \cdot 1 0^{- 4})

lo g_{10} (a b^{2})

ln (x^{6} y^{3})

lo g_{10} (\frac{y ^{2}}{z})

What is simplify-log_{10}(8*10^{-9}) ?
The solution to simplify-log_{10}(8*10^{-9}) is -3log_{10}(2)+9