What is 3log_{5}(a)-log_{5}(b) ?

The solution to 3log_{5}(a)-log_{5}(b) is log_{5}((a^3)/b)

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simplify 3log_{5}(a)-log_{5}(b)

simplify

3 lo g_{5} (a) - lo g_{5} (b)

lo g_{5} (\frac{a ^{3}}{b})

Solution steps

3 lo g_{5} (a) - lo g_{5} (b)

Apply log rule:

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

3 lo g_{5} (a) = lo g_{5} (a^{3})

= lo g_{5} (a^{3}) - lo g_{5} (b)

Apply log rule:

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

lo g_{5} (a^{3}) - lo g_{5} (b) = lo g_{5} (\frac{a ^{3}}{b})

= lo g_{5} (\frac{a ^{3}}{b})

ln (\frac{t}{2 t + 3})

lo g_{8} (\frac{64}{x + 1})

9 ln (a) - 6 ln (b)

2 lo g_{10} (2) + 2 lo g_{10} (3)

What is 3log_{5}(a)-log_{5}(b) ?
The solution to 3log_{5}(a)-log_{5}(b) is log_{5}((a^3)/b)