What is log_{10}((2a^2)/3) ?

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

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simplify log_{10}((2a^2)/3)

simplify

lo g_{10} (\frac{2 a ^{2}}{3})

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

Solution steps

lo g_{10} (\frac{2 a ^{2}}{3})

Apply log rule:

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

lo g_{10} (\frac{2 a ^{2}}{3}) = lo g_{10} (2 a^{2}) - lo g_{10} (3)

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

Simplify

lo g_{10} (2 a^{2}) : lo g_{10} (2) + 2 lo g_{10} (a)

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

5 ln (z) - 3 ln (x) - 7 ln (y)

lo g_{5} (3 x + 1) + lo g_{5} (x)

lo g_{10} (8) + lo g_{10} (3)

lo g_{3} (12) + lo g_{3} (7) + 4 lo g_{3} (5)

- lo g_{10} (4 \cdot 1 0^{- 8})

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