What is 4log_{b}(q)-log_{b}(r) ?

The solution to 4log_{b}(q)-log_{b}(r) is log_{b}((q^4)/r)

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simplify 4log_{b}(q)-log_{b}(r)

simplify

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

lo g_{b} (\frac{q ^{4}}{r})

Solution steps

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

Apply log rule:

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

4 lo g_{b} (q) = lo g_{b} (q^{4})

= lo g_{b} (q^{4}) - 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^{4}) - lo g_{b} (r) = lo g_{b} (\frac{q ^{4}}{r})

= lo g_{b} (\frac{q ^{4}}{r})

ln (x x^{2} - 8)

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

ln (\frac{1}{16 e ^{2}})

10 lo g_{10} (x) - 2 lo g_{10} (x^{2})

lo g_{10} (\frac{c}{a ^{4} b ^{4}})

What is 4log_{b}(q)-log_{b}(r) ?
The solution to 4log_{b}(q)-log_{b}(r) is log_{b}((q^4)/r)