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

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

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

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

lo g_{3} (2 x) - 5 lo g_{3} (y)

- lo g_{10} (2 \times 1 0^{- 5})

2 lo g_{6} (5 a) + lo g_{6} (b) + 7 lo g_{6} (c)

ln (- 1) + ln (- 3)

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