What is simplify-log_{10}(2.09(10^{-12})) ?

The solution to simplify-log_{10}(2.09(10^{-12})) is -log_{10}(2.09)+12

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simplify-log_{10}(2.09(10^{-12}))

simplify

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

- lo g_{10} (2.09) + 12

Decimal Notation

11.67985 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= - (lo g_{10} (2.09) - 12 lo g_{10} (10))

12 lo g_{10} (10) = 12

= - (lo g_{10} (2.09) - 12)

Distribute parentheses

= - (lo g_{10} (2.09)) - (- 12)

Apply minus-plus rules

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

= - lo g_{10} (2.09) + 12

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

ln (\frac{1}{- 311})

ln (\frac{4 x}{( 1 - y )})

ln (\frac{x - 8}{x + 2})

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

What is simplify-log_{10}(2.09(10^{-12})) ?
The solution to simplify-log_{10}(2.09(10^{-12})) is -log_{10}(2.09)+12