What is log_{10}(2x^{-3}) ?

The solution to log_{10}(2x^{-3}) is log_{10}(2)-3log_{10}(x)

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simplify log_{10}(2x^{-3})

simplify

lo g_{10} (2 x^{- 3})

lo g_{10} (2) - 3 lo g_{10} (x)

Solution steps

lo g_{10} (2 x^{- 3})

Simplify

2 x^{- 3} : \frac{2}{x ^{3}}

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

Apply log rule:

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

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

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

Simplify

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

= lo g_{10} (2) - 3 lo g_{10} (x)

lo g_{2} (8 x)

lo g_{10} (10000 y)

ln (6.57 \cdot 1 0^{- 2})

lo g_{7} (2) + lo g_{7} (11)

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