What is 7log_{5}(p)-log_{5}(q) ?

The solution to 7log_{5}(p)-log_{5}(q) is log_{5}((p^7)/q)

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simplify 7log_{5}(p)-log_{5}(q)

simplify

7 lo g_{5} (p) - lo g_{5} (q)

lo g_{5} (\frac{p ^{7}}{q})

Solution steps

7 lo g_{5} (p) - lo g_{5} (q)

Apply log rule:

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

7 lo g_{5} (p) = lo g_{5} (p^{7})

= lo g_{5} (p^{7}) - lo g_{5} (q)

Apply log rule:

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

lo g_{5} (p^{7}) - lo g_{5} (q) = lo g_{5} (\frac{p ^{7}}{q})

= lo g_{5} (\frac{p ^{7}}{q})

\frac{1}{2} ln (\frac{x + 1}{x - 1}) + e^{s i n (x^{2})} + ln (3)

ln (x^{4})

3 ln (x) - \frac{1}{2} ln (y)

ln (0.15) - ln (0.25)

lo g_{b} (z^{4} y)

What is 7log_{5}(p)-log_{5}(q) ?
The solution to 7log_{5}(p)-log_{5}(q) is log_{5}((p^7)/q)