What is log_{b}(8)-log_{b}(4)-2log_{b}(3) ?

The solution to log_{b}(8)-log_{b}(4)-2log_{b}(3) is log_{b}(2/9)

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simplify log_{b}(8)-log_{b}(4)-2log_{b}(3)

simplify

lo g_{b} (8) - lo g_{b} (4) - 2 lo g_{b} (3)

lo g_{b} (\frac{2}{9})

Solution steps

lo g_{b} (8) - lo g_{b} (4) - 2 lo g_{b} (3)

Apply log rule:

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

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

= lo g_{b} (8) - lo g_{b} (4) - lo g_{b} (3^{2})

Apply log rule:

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

lo g_{b} (8) - lo g_{b} (4) = lo g_{b} (\frac{8}{4})

= lo g_{b} (\frac{8}{4}) - lo g_{b} (3^{2})

Apply log rule:

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

lo g_{b} (\frac{8}{4}) - lo g_{b} (3^{2}) = lo g_{b} (\frac{\frac{8}{4}}{3 ^{2}})

= lo g_{b} (\frac{\frac{8}{4}}{3 ^{2}})

\frac{\frac{8}{4}}{3 ^{2}} = \frac{2}{9}

= lo g_{b} (\frac{2}{9})

ln (\frac{e ^{2}}{2})

lo g_{9} (1 1^{3} \cdot 7^{4})

ln (600) - ln (300)

lo g_{4} (\frac{( x + 2 ) ^{2}}{2 x})

2 ln (6 x)

What is log_{b}(8)-log_{b}(4)-2log_{b}(3) ?
The solution to log_{b}(8)-log_{b}(4)-2log_{b}(3) is log_{b}(2/9)