What is log_{10}(1/2)+log_{10}(4)-2 ?

The solution to log_{10}(1/2)+log_{10}(4)-2 is log_{10}(2)-2

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simplify log_{10}(1/2)+log_{10}(4)-2

simplify

lo g_{10} (\frac{1}{2}) + lo g_{10} (4) - 2

lo g_{10} (2) - 2

Decimal

- 1.69897 \dots

Solution steps

lo g_{10} (\frac{1}{2}) + lo g_{10} (4) - 2

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (\frac{1}{2}) + lo g_{10} (4) = lo g_{10} (\frac{1}{2} \cdot 4)

= lo g_{10} (\frac{1}{2} \cdot 4) - 2

\frac{1}{2} \cdot 4 = 2

= lo g_{10} (2) - 2

ln (\frac{8}{9 x ^{9} y})

lo g_{b} (6) + lo g_{b} (4)

\frac{1}{2} ln (8) - ln (32)

ln (\frac{b}{a})

lo g_{2} (\frac{x ^{2}}{x ^{3} + 1})

What is log_{10}(1/2)+log_{10}(4)-2 ?
The solution to log_{10}(1/2)+log_{10}(4)-2 is log_{10}(2)-2