What is log_{4}(x)+6log_{4}(y)+3log_{4}(z) ?

The solution to log_{4}(x)+6log_{4}(y)+3log_{4}(z) is log_{4}(xy^6z^3)

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simplify log_{4}(x)+6log_{4}(y)+3log_{4}(z)

simplify

lo g_{4} (x) + 6 lo g_{4} (y) + 3 lo g_{4} (z)

lo g_{4} (x y^{6} z^{3})

Solution steps

lo g_{4} (x) + 6 lo g_{4} (y) + 3 lo g_{4} (z)

Apply log rule:

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

6 lo g_{4} (y) = lo g_{4} (y^{6})

= lo g_{4} (x) + lo g_{4} (y^{6}) + 3 lo g_{4} (z)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{4} (x) + lo g_{4} (y^{6}) = lo g_{4} (x y^{6})

= lo g_{4} (x y^{6}) + 3 lo g_{4} (z)

Apply log rule:

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

3 lo g_{4} (z) = lo g_{4} (z^{3})

= lo g_{4} (x y^{6}) + lo g_{4} (z^{3})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{4} (x y^{6}) + lo g_{4} (z^{3}) = lo g_{4} (x y^{6} z^{3})

= lo g_{4} (x y^{6} z^{3})

\frac{1}{2} (ln (e^{2} + 1) - ln (2))

lo g_{6} (\frac{6}{x})

- 100 ln (\frac{1}{100})

ln (\frac{1}{1 - 0.6})

sec (3 x + 1) - ln (3 x)

What is log_{4}(x)+6log_{4}(y)+3log_{4}(z) ?
The solution to log_{4}(x)+6log_{4}(y)+3log_{4}(z) is log_{4}(xy^6z^3)