What is log_{10}(a)-3log_{10}(b)-3 ?

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

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simplify log_{10}(a)-3log_{10}(b)-3

simplify

lo g_{10} (a) - 3 lo g_{10} (b) - 3

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

Solution steps

lo g_{10} (a) - 3 lo g_{10} (b) - 3

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{10} (b) = lo g_{10} (b^{3})

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

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

- ln (10 \cdot 1 0^{- 6})

ln (9) + 4 ln (2)

ln (x^{2} + 2 x + 1) - ln (x + 1)

lo g_{b} (0.44) + lo g_{b} (0.89)

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