What is 4log_{6}(r)-3log_{6}(s)-2log_{6}(t) ?

The solution to 4log_{6}(r)-3log_{6}(s)-2log_{6}(t) is log_{6}((r^4)/(s^3t^2))

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simplify 4log_{6}(r)-3log_{6}(s)-2log_{6}(t)

simplify

4 lo g_{6} (r) - 3 lo g_{6} (s) - 2 lo g_{6} (t)

lo g_{6} (\frac{r ^{4}}{s ^{3} t ^{2}})

Solution steps

4 lo g_{6} (r) - 3 lo g_{6} (s) - 2 lo g_{6} (t)

4 lo g_{6} (r) = lo g_{6} (r^{4})

- 3 lo g_{6} (s) = - lo g_{6} (s^{3})

- 2 lo g_{6} (t) = - lo g_{6} (t^{2})

= lo g_{6} (r^{4}) - lo g_{6} (s^{3}) - lo g_{6} (t^{2})

Apply log rule:

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

lo g_{6} (r^{4}) - lo g_{6} (s^{3}) = lo g_{6} (\frac{r ^{4}}{s ^{3}})

= lo g_{6} (\frac{r ^{4}}{s ^{3}}) - lo g_{6} (t^{2})

Apply log rule:

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

lo g_{6} (\frac{r ^{4}}{s ^{3}}) - lo g_{6} (t^{2}) = lo g_{6} (\frac{\frac{r ^{4}}{s ^{3}}}{t ^{2}})

= lo g_{6} (\frac{\frac{r ^{4}}{s ^{3}}}{t ^{2}})

Simplify

\frac{\frac{r ^{4}}{s ^{3}}}{t ^{2}} : \frac{r ^{4}}{s ^{3} t ^{2}}

= lo g_{6} (\frac{r ^{4}}{s ^{3} t ^{2}})

ln (\frac{2 ^{4}}{3 ^{3} 5 ^{2}})

lo g_{a} (x \times y)

lo g_{2} (a) - lo g_{2} (b)

lo g_{b} (5 x \cdot 3 y)

lo g_{b} (3) + lo g_{b} (6)

What is 4log_{6}(r)-3log_{6}(s)-2log_{6}(t) ?
The solution to 4log_{6}(r)-3log_{6}(s)-2log_{6}(t) is log_{6}((r^4)/(s^3t^2))