What is 9log_{5}(x)+3log_{5}(y) ?

The solution to 9log_{5}(x)+3log_{5}(y) is log_{5}(x^9y^3)

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simplify 9log_{5}(x)+3log_{5}(y)

simplify

9 lo g_{5} (x) + 3 lo g_{5} (y)

lo g_{5} (x^{9} y^{3})

Solution steps

9 lo g_{5} (x) + 3 lo g_{5} (y)

Apply log rule:

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

9 lo g_{5} (x) = lo g_{5} (x^{9})

= lo g_{5} (x^{9}) + 3 lo g_{5} (y)

Apply log rule:

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

3 lo g_{5} (y) = lo g_{5} (y^{3})

= lo g_{5} (x^{9}) + lo g_{5} (y^{3})

Apply log rule:

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

lo g_{5} (x^{9}) + lo g_{5} (y^{3}) = lo g_{5} (x^{9} y^{3})

= lo g_{5} (x^{9} y^{3})

3 ln (\frac{1}{3}) - ln (\frac{1}{3})

64 \cdot ln (\frac{4}{25})

2 lo g_{e} (6) + 2 lo g_{e} (π) - lo g_{e} (5)

3 ln (x) - 2 ln (x + 1)

lo g_{10} (\frac{z}{y})

What is 9log_{5}(x)+3log_{5}(y) ?
The solution to 9log_{5}(x)+3log_{5}(y) is log_{5}(x^9y^3)