What is log_{b}(15)-3log_{b}(12) ?

The solution to log_{b}(15)-3log_{b}(12) is log_{b}(5/576)

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simplify log_{b}(15)-3log_{b}(12)

simplify

lo g_{b} (15) - 3 lo g_{b} (12)

lo g_{b} (\frac{5}{576})

Solution steps

lo g_{b} (15) - 3 lo g_{b} (12)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

- 3 lo g_{b} (12) = - lo g_{b} (1 2^{3})

= lo g_{b} (15) - lo g_{b} (1 2^{3})

Apply log rule:

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

lo g_{b} (15) - lo g_{b} (1 2^{3}) = lo g_{b} (\frac{15}{1 2 ^{3}})

= lo g_{b} (\frac{15}{1 2 ^{3}})

Cancel

\frac{15}{1 2 ^{3}} : \frac{5}{576}

= lo g_{b} (\frac{5}{576})

2 lo g_{10} (5) - 2 lo g_{10} (x)

ln (2 u) - ln (\frac{u}{2})

lo g_{a} (3 x yz)

14 + lo g_{10} (1.8 \cdot 1 0^{- 5})

ln (\frac{2 ^{- 3}}{3 ^{2} 5 - 2})

What is log_{b}(15)-3log_{b}(12) ?
The solution to log_{b}(15)-3log_{b}(12) is log_{b}(5/576)