What is log_{4}(13b^8c) ?

The solution to log_{4}(13b^8c) is log_{4}(13)+8log_{4}(b)+log_{4}(c)

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simplify log_{4}(13b^8c)

simplify

lo g_{4} (13 b^{8} c)

lo g_{4} (13) + 8 lo g_{4} (b) + lo g_{4} (c)

Solution steps

lo g_{4} (13 b^{8} c)

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{4} (13 b^{8} c) = lo g_{4} (13) + lo g_{4} (b^{8}) + lo g_{4} (c)

= lo g_{4} (13) + lo g_{4} (b^{8}) + lo g_{4} (c)

Simplify

lo g_{4} (b^{8}) : 8 lo g_{4} (b)

= lo g_{4} (13) + 8 lo g_{4} (b) + lo g_{4} (c)

lo g_{9} (\frac{9}{x})

ln (x) - 8 ln (x + 5)

lo g_{5} (\frac{125}{x})

5 ln (x) - \frac{1}{2} ln (y)

lo g_{b} (\frac{x ^{2} y}{z ^{7}})

What is log_{4}(13b^8c) ?
The solution to log_{4}(13b^8c) is log_{4}(13)+8log_{4}(b)+log_{4}(c)