What is 3log_{10}(r)-2log_{10}(s)+log_{10}(t) ?

The solution to 3log_{10}(r)-2log_{10}(s)+log_{10}(t) is log_{10}((r^3t)/(s^2))

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simplify 3log_{10}(r)-2log_{10}(s)+log_{10}(t)

simplify

3 lo g_{10} (r) - 2 lo g_{10} (s) + lo g_{10} (t)

lo g_{10} (\frac{r ^{3} t}{s ^{2}})

Solution steps

3 lo g_{10} (r) - 2 lo g_{10} (s) + lo g_{10} (t)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 lo g_{10} (r) = lo g_{10} (r^{3})

= lo g_{10} (r^{3}) - 2 lo g_{10} (s) + lo g_{10} (t)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{10} (s) = lo g_{10} (s^{2})

= lo g_{10} (r^{3}) - lo g_{10} (s^{2}) + lo g_{10} (t)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (r^{3}) - lo g_{10} (s^{2}) = lo g_{10} (\frac{r ^{3}}{s ^{2}})

= lo g_{10} (\frac{r ^{3}}{s ^{2}}) + lo g_{10} (t)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (\frac{r ^{3}}{s ^{2}}) + lo g_{10} (t) = lo g_{10} (\frac{r ^{3}}{s ^{2}} t)

= lo g_{10} (\frac{r ^{3}}{s ^{2}} t)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{10} (\frac{r ^{3} t}{s ^{2}})

ln (\frac{x ^{5} - 5}{x})

ln (\frac{0.75}{1})

2 lo g_{b} (x) - 2 lo g_{b} (y) + lo g_{b} (z)

2 ln (5) - ln (3)

\frac{1}{3} \cdot lo g_{10} (x^{3} + 1) + \frac{1}{2} lo g_{10} (x^{2} + 1)

What is 3log_{10}(r)-2log_{10}(s)+log_{10}(t) ?
The solution to 3log_{10}(r)-2log_{10}(s)+log_{10}(t) is log_{10}((r^3t)/(s^2))