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

The solution to log_{10}((x^2)/5) is 2log_{10}(x)-log_{10}(5)

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simplify log_{10}((x^2)/5)

simplify

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

2 lo g_{10} (x) - lo g_{10} (5)

Solution steps

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (x^{2}) : 2 lo g_{10} (x)

= 2 lo g_{10} (x) - lo g_{10} (5)

- lo g_{10} (1 \cdot 1 0^{- 9})

lo g_{10} (5 x^{3})

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

ln (3 x)

What is log_{10}((x^2)/5) ?
The solution to log_{10}((x^2)/5) is 2log_{10}(x)-log_{10}(5)