What is 7log_{a}(m)-1/3 log_{a}(r) ?

The solution to 7log_{a}(m)-1/3 log_{a}(r) is log_{a}((m^7r^{2/3})/r)

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simplify 7log_{a}(m)-1/3 log_{a}(r)

simplify

7 lo g_{a} (m) - \frac{1}{3} lo g_{a} (r)

lo g_{a} (\frac{m ^{7} r ^{\frac{2}{3}}}{r})

Solution steps

7 lo g_{a} (m) - \frac{1}{3} lo g_{a} (r)

Apply log rule:

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

7 lo g_{a} (m) = lo g_{a} (m^{7})

= lo g_{a} (m^{7}) - \frac{1}{3} lo g_{a} (r)

Apply log rule:

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

\frac{1}{3} lo g_{a} (r) = lo g_{a} (r^{\frac{1}{3}})

= lo g_{a} (m^{7}) - lo g_{a} (r^{\frac{1}{3}})

Apply log rule:

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

lo g_{a} (m^{7}) - lo g_{a} (r^{\frac{1}{3}}) = lo g_{a} (\frac{m ^{7}}{r ^{\frac{1}{3}}})

= lo g_{a} (\frac{m ^{7}}{r ^{\frac{1}{3}}})

Simplify

\frac{m ^{7}}{r ^{\frac{1}{3}}} : \frac{m ^{7} r ^{\frac{2}{3}}}{r}

= lo g_{a} (\frac{m ^{7} r ^{\frac{2}{3}}}{r})

ln (\frac{29}{22.6})

4 \cdot lo g_{10} (43488 3 \cdot 1 0^{- 2}) - 4

- \frac{2}{3} lo g_{3} (3 m^{2}) + \frac{1}{2} lo g_{3} (9 m^{2})

5 lo g_{10} (k) - lo g_{10} (q)

lo g_{10} (\frac{a ^{5} b ^{7}}{c ^{2}})

What is 7log_{a}(m)-1/3 log_{a}(r) ?
The solution to 7log_{a}(m)-1/3 log_{a}(r) is log_{a}((m^7r^{2/3})/r)