What is log_{5}((25a^5b^8)/(sqrt(cd))) ?

The solution to log_{5}((25a^5b^8)/(sqrt(cd))) is 2+5log_{5}(a)+8log_{5}(b)-log_{5}(sqrt(cd))

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simplify log_{5}((25a^5b^8)/(sqrt(cd)))

simplify

lo g_{5} (\frac{25 a ^{5} b ^{8}}{c d})

2 + 5 lo g_{5} (a) + 8 lo g_{5} (b) - lo g_{5} (c d)

Solution steps

lo g_{5} (\frac{25 a ^{5} b ^{8}}{c d})

Apply log rule:

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

lo g_{5} (\frac{25 a ^{5} b ^{8}}{c d}) = lo g_{5} (25 a^{5} b^{8}) - lo g_{5} (c d)

= lo g_{5} (25 a^{5} b^{8}) - lo g_{5} (c d)

Simplify

lo g_{5} (25 a^{5} b^{8}) : 2 + 5 lo g_{5} (a) + 8 lo g_{5} (b)

= 2 + 5 lo g_{5} (a) + 8 lo g_{5} (b) - lo g_{5} (c d)

ln (\frac{3 x}{x ^{2} + 4})

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

ln (e (x + 9))

lo g_{10} (m) - lo g_{10} (n) + lo g_{10} (p)

ln (\frac{x}{1 + x})

What is log_{5}((25a^5b^8)/(sqrt(cd))) ?
The solution to log_{5}((25a^5b^8)/(sqrt(cd))) is 2+5log_{5}(a)+8log_{5}(b)-log_{5}(sqrt(cd))