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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

3 lo g_{x} (y) = lo g_{x} (y^{3})

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

Apply log rule:

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

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

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

ln (\frac{x}{y} + 2) - ln (y)

ln (e^{v} (p^{d} q^{1 - d}))

ln (\frac{9}{5}) - \frac{16}{45}

ln (\frac{1000}{25})

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

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