What is log_{10}((sqrt(10a\sqrt{0.1)})/(10)) ?

The solution to log_{10}((sqrt(10a\sqrt{0.1)})/(10)) is log_{10}(sqrt(10)sqrt(\sqrt{0.1)a})-1

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simplify log_{10}((sqrt(10a\sqrt{0.1)})/(10))

simplify

lo g_{10} (\frac{10 a 0.1}{10})

lo g_{10} (10 0.1 a) - 1

Solution steps

lo g_{10} (\frac{10 a 0.1}{10})

Apply log rule:

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

lo g_{10} (\frac{10 a 0.1}{10}) = lo g_{10} (10 a 0.1) - lo g_{10} (10)

= lo g_{10} (10 0.1 a) - lo g_{10} (10)

10 a 0.1 = 10 0.1 a

= lo g_{10} (10 0.1 a) - lo g_{10} (10)

Apply log rule:

lo g_{a} (a) = 1

= lo g_{10} (10 0.1 a) - 1

- lo g_{10} (4.1 \cdot 1 0^{- 3})

4 lo g_{10} (3 x^{3}) - \frac{1}{2} lo g_{10} (9 x^{8})

lo g_{10} (81) - lo g_{10} (\frac{64}{36})

5 ln (a) + \frac{ln ( b )}{3} - 3 ln (c)

ln (\frac{1}{72})

What is log_{10}((sqrt(10a\sqrt{0.1)})/(10)) ?
The solution to log_{10}((sqrt(10a\sqrt{0.1)})/(10)) is log_{10}(sqrt(10)sqrt(\sqrt{0.1)a})-1