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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

\frac{1}{2} ln (x + 1) - \frac{1}{4} ln (x^{2} + 1)

5 lo g_{10} (a) - 25 lo g_{10} (b)

2 lo g_{m} (a) - 3 lo g_{m} (b^{2})

\frac{2}{3} lo g_{b} (27) + 2 lo g_{b} (2) - lo g_{b} (3)

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