What is 5log_{b}(q)-log_{b}(r) ?

The solution to 5log_{b}(q)-log_{b}(r) is log_{b}((q^5)/r)

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simplify 5log_{b}(q)-log_{b}(r)

simplify

5 lo g_{b} (q) - lo g_{b} (r)

lo g_{b} (\frac{q ^{5}}{r})

Solution steps

5 lo g_{b} (q) - lo g_{b} (r)

Apply log rule:

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

5 lo g_{b} (q) = lo g_{b} (q^{5})

= lo g_{b} (q^{5}) - lo g_{b} (r)

Apply log rule:

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

lo g_{b} (q^{5}) - lo g_{b} (r) = lo g_{b} (\frac{q ^{5}}{r})

= lo g_{b} (\frac{q ^{5}}{r})

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

lo g_{10} (x (x + 1)^{4})

lo g_{3} ((x - 8)^{2})

ln (1025) - ln (2)

lo g_{4} (16) - lo g_{4} (20) - lo g_{4} (5)

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