What is log_{10}((10^{-10})/2) ?

The solution to log_{10}((10^{-10})/2) is -10-log_{10}(2)

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simplify log_{10}((10^{-10})/2)

simplify

lo g_{10} (\frac{1 0 ^{- 10}}{2})

- 10 - lo g_{10} (2)

Decimal Notation

- 10.30102 \dots

Solution steps

lo g_{10} (\frac{1 0 ^{- 10}}{2})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{1 0 ^{- 10}}{2}) = lo g_{10} (1 0^{- 10}) - lo g_{10} (2)

= lo g_{10} (1 0^{- 10}) - lo g_{10} (2)

Apply log rule:

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

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

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

10 lo g_{10} (10) = 10

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

ln ((- 1) e^{x})

ln (e ln (\frac{1}{e}))

- lo g_{10} (1.15 \cdot 1 0^{- 3})

- lo g_{10} (5.5 \cdot 1 0^{- 4})

ln (7.5 \cdot 1 0^{- 6})

What is log_{10}((10^{-10})/2) ?
The solution to log_{10}((10^{-10})/2) is -10-log_{10}(2)