What is log_{10}(2)-log_{10}(20.2) ?

The solution to log_{10}(2)-log_{10}(20.2) is log_{10}(0.09900…)

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simplify log_{10}(2)-log_{10}(20.2)

simplify

lo g_{10} (2) - lo g_{10} (20.2)

lo g_{10} (0.09900 \dots)

Decimal Notation

- 1.00432 \dots

Solution steps

lo g_{10} (2) - lo g_{10} (20.2)

Apply log rule:

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

lo g_{10} (2) - lo g_{10} (20.2) = lo g_{10} (\frac{2}{20.2})

= lo g_{10} (\frac{2}{20.2})

Divide the numbers:

\frac{2}{20.2} = 0.09900 \dots

= lo g_{10} (0.09900 \dots)

- 50 ln (\frac{2}{3})

- lo g_{10} (1.17 \cdot 1 0^{- 6})

ln (\frac{20000}{477})

ln (θ \cdot e^{- θ x})

lo g_{5} (5 e^{10} \cdot 125)

What is log_{10}(2)-log_{10}(20.2) ?
The solution to log_{10}(2)-log_{10}(20.2) is log_{10}(0.09900…)