What is log_{5}((a^8)/(b^7c)) ?

The solution to log_{5}((a^8)/(b^7c)) is 8log_{5}(a)-7log_{5}(b)-log_{5}(c)

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simplify log_{5}((a^8)/(b^7c))

simplify

lo g_{5} (\frac{a ^{8}}{b ^{7} c})

8 lo g_{5} (a) - 7 lo g_{5} (b) - lo g_{5} (c)

Solution steps

lo g_{5} (\frac{a ^{8}}{b ^{7} c})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{5} (\frac{a ^{8}}{b ^{7} c}) = lo g_{5} (a^{8}) - lo g_{5} (b^{7} c)

= lo g_{5} (a^{8}) - lo g_{5} (b^{7} c)

lo g_{5} (a^{8}) = 8 lo g_{5} (a)

lo g_{5} (b^{7} c) = 7 lo g_{5} (b) + lo g_{5} (c)

= 8 lo g_{5} (a) - (7 lo g_{5} (b) + lo g_{5} (c))

Apply the distributive law:

- (a + b) = - a - b

- (7 lo g_{5} (b) + lo g_{5} (c)) = - 7 lo g_{5} (b) - lo g_{5} (c)

= 8 lo g_{5} (a) - 7 lo g_{5} (b) - lo g_{5} (c)

ln (2 e^{- 2 x})

ln (x) - 2 [ln (x + 2) + ln (x - 2)]

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

3 lo g_{b} (x) + 2 lo g_{b} (y) - \frac{1}{2} lo g_{b} (z)

lo g_{10} (\frac{x ^{3} y}{z})

What is log_{5}((a^8)/(b^7c)) ?
The solution to log_{5}((a^8)/(b^7c)) is 8log_{5}(a)-7log_{5}(b)-log_{5}(c)