What is log_{10}((2a^5)/(27)) ?

The solution to log_{10}((2a^5)/(27)) is log_{10}(2)+5log_{10}(a)-3log_{10}(3)

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simplify log_{10}((2a^5)/(27))

simplify

lo g_{10} (\frac{2 a ^{5}}{27})

lo g_{10} (2) + 5 lo g_{10} (a) - 3 lo g_{10} (3)

Solution steps

lo g_{10} (\frac{2 a ^{5}}{27})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{2 a ^{5}}{27}) = lo g_{10} (2 a^{5}) - lo g_{10} (27)

= lo g_{10} (2 a^{5}) - lo g_{10} (27)

lo g_{10} (2 a^{5}) = lo g_{10} (2) + 5 lo g_{10} (a)

lo g_{10} (27) = 3 lo g_{10} (3)

= lo g_{10} (2) + 5 lo g_{10} (a) - 3 lo g_{10} (3)

lo g_{6} (30) - lo g_{6} (10)

- ln (\frac{a}{b})

- lo g_{10} (2.7 \cdot 1 0^{- 3})

What is log_{10}((2a^5)/(27)) ?
The solution to log_{10}((2a^5)/(27)) is log_{10}(2)+5log_{10}(a)-3log_{10}(3)