What is 7log_{2}(r)-8log_{2}(s)-2log_{2}(t) ?

The solution to 7log_{2}(r)-8log_{2}(s)-2log_{2}(t) is log_{2}((r^7)/(s^8t^2))

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simplify 7log_{2}(r)-8log_{2}(s)-2log_{2}(t)

simplify

7 lo g_{2} (r) - 8 lo g_{2} (s) - 2 lo g_{2} (t)

lo g_{2} (\frac{r ^{7}}{s ^{8} t ^{2}})

Solution steps

7 lo g_{2} (r) - 8 lo g_{2} (s) - 2 lo g_{2} (t)

7 lo g_{2} (r) = lo g_{2} (r^{7})

- 8 lo g_{2} (s) = - lo g_{2} (s^{8})

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

= lo g_{2} (r^{7}) - lo g_{2} (s^{8}) - lo g_{2} (t^{2})

Apply log rule:

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

lo g_{2} (r^{7}) - lo g_{2} (s^{8}) = lo g_{2} (\frac{r ^{7}}{s ^{8}})

= lo g_{2} (\frac{r ^{7}}{s ^{8}}) - lo g_{2} (t^{2})

Apply log rule:

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

lo g_{2} (\frac{r ^{7}}{s ^{8}}) - lo g_{2} (t^{2}) = lo g_{2} (\frac{\frac{r ^{7}}{s ^{8}}}{t ^{2}})

= lo g_{2} (\frac{\frac{r ^{7}}{s ^{8}}}{t ^{2}})

Simplify

\frac{\frac{r ^{7}}{s ^{8}}}{t ^{2}} : \frac{r ^{7}}{s ^{8} t ^{2}}

= lo g_{2} (\frac{r ^{7}}{s ^{8} t ^{2}})

6 ln (z) - \frac{1}{7} ln (x) + 6 ln (y)

lo g_{7} (2 y)

lo g_{10} (\frac{11 x}{13})

lo g_{10} (1 + 3) \cdot lo g_{10} (\frac{4}{3})

lo g_{2} (\frac{8 x ^{2}}{y})

What is 7log_{2}(r)-8log_{2}(s)-2log_{2}(t) ?
The solution to 7log_{2}(r)-8log_{2}(s)-2log_{2}(t) is log_{2}((r^7)/(s^8t^2))